diff --git a/.gitmodules b/.gitmodules new file mode 100644 index 0000000..b1e2a35 --- /dev/null +++ b/.gitmodules @@ -0,0 +1,6 @@ +[submodule "bibliography"] + path = bibliography + url = git@git.cplx.vm.uni-freiburg.de:kebekus/bibliography.git +[submodule "tex"] + path = tex + url = git@git.cplx.vm.uni-freiburg.de:kebekus/tex.git diff --git a/.vscode/ltex.dictionary.de-DE.txt b/.vscode/ltex.dictionary.de-DE.txt index 36836c9..38e8b91 100644 --- a/.vscode/ltex.dictionary.de-DE.txt +++ b/.vscode/ltex.dictionary.de-DE.txt @@ -63,3 +63,67 @@ Teilbarkeitseigenschaften kgV faktoriellen Geodät +Quotientenkörper +Quotientenkörpers +Irreduzibilitätskriterien +Irreduzibilitätskriterium +Teilbarkeitsbetrachtungen +Teilerpolynome +Lodovico +Lagrangia +Interpolationsformel +Schönemann +Driesen +Friedebergischer +reduzibel +Einsetzungskomposition +Substitutionsmorphismus +Konstruierbarkeitsfragen +konjungierte +konstruierbare +Konstruierbarkeitsfrage +transzendent +Rechtsideale +Sorau +Dedekind +nicht-faktoriellen +Hauptideale +Erzeugendensysteme +Gödelschen +Erzeugendensystems +Erzeugendensystem +Teiler- +Hauptidealen +Faktorialität +Quotientenvektoraumes +Quotientenvektorräumen +Quotientenvektorräume +Quotientenring +Repräsentantensystems +Homomorphiesatzes +Homomorphiesatz +Quotientenabbildung +Urbildmenge +Primideale +Primideals +Primideal +Summenideal +Teilerfremdheit +Funktionenkörper +Kodierungstheorie +Substitutionsabbildung +Steinitz +Laurahütte +nicht-Kanonizität +Zerfällungskörpern +inseparable +Teilbarkeitsrelationen +Frobenius-Morphismus +Frobenius-Endomorphismus +Einselements +separabel +inseparabel +Separabilität +Substitutionsmorphismen +Separabilitätsgrad +inseparablen diff --git a/.vscode/ltex.hiddenFalsePositives.de-DE.txt b/.vscode/ltex.hiddenFalsePositives.de-DE.txt index b9b07c3..7d46580 100644 --- a/.vscode/ltex.hiddenFalsePositives.de-DE.txt +++ b/.vscode/ltex.hiddenFalsePositives.de-DE.txt @@ -24,3 +24,32 @@ {"rule":"DE_SENTENCE_WHITESPACE","sentence":"^\\QVorlesung 6\\E$"} {"rule":"UPPERCASE_SENTENCE_START","sentence":"^\\QggT und kgV.\\E$"} {"rule":"GERMAN_WORD_REPEAT_BEGINNING_RULE","sentence":"^\\QEs ist \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q genau dann, wenn für alle \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q gilt, dass \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ist.\\E$"} +{"rule":"KLEINSCHREIBUNG_KEIN_NAME","sentence":"^\\QWenn Sie bei mir die Vorlesung „Lineare Algebra“ gehört haben, dann wird Ihnen die folgende Definition sehr vertraut vorkommen.\\E$"} +{"rule":"DE_CASE","sentence":"^\\Q[Anwenden eines Ringhomomorphismus auf die Koeffizienten:] Ist \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ein Ringhomomorphismus, dann ist auch \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ein Ringmorphismus.\\E$"} +{"rule":"DE_CASE","sentence":"^\\QSetze \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q [Substitutionsmorphismus] Es sei ein Element \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q gegeben.\\E$"} +{"rule":"DE_CASE","sentence":"^\\Q[Anwenden eines Ringhomomorphismus auf die Koeffizienten] Ist \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ein Ringhomomorphismus, dann ist auch \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ein Ringmorphismus.\\E$"} +{"rule":"KLEINSCHREIBUNG_KEIN_NAME","sentence":"^\\QIch verzichte deshalb im Folgenden sehr oft auf Beweise und behaupte, dass „alles genau so geht, wie in der Linearen Algebra“.\\E$"} +{"rule":"KLEINSCHREIBUNG_KEIN_NAME","sentence":"^\\QStellen Sie sicher, dass sie sich noch ausreichend gut an die Vorlesung „Lineare Algebra“ erinnern.\\E$"} +{"rule":"KLEINSCHREIBUNG_KEIN_NAME","sentence":"^\\QGenau wie die Quotientenvektorräume der Linearen Algebra sind Restklassenringe durch folgende universelle Eigenschaft definiert.\\E$"} +{"rule":"DE_SUBJECT_VERB_AGREEMENT","sentence":"^\\QEin Restklassenring oder Quotientenring ist ein kommutativer Ring \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q mit Eins zusammen mit einem Ringmorphismus \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, sodass \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ist und so, dass die folgende universelle Eigenschaft gilt: ist \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ein weiterer Ringmorphismus mit \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, dann gibt es genau einen Ringmorphismus \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q, sodass das folgende Diagramm kommutiert, \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"} +{"rule":"KLEINSCHREIBUNG_KEIN_NAME","sentence":"^\\QErinnerung an die Lineare Algebra: Quotient nach Äquivalenzrelation = \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q = Menge der Äquivalenzklassen\\E$"} +{"rule":"KLEINSCHREIBUNG_KEIN_NAME","sentence":"^\\QDer folgende Satz folgt wie in der Linearen Algebra aus der universellen Eigenschaft.\\E$"} +{"rule":"DE_CASE","sentence":"^\\Q[Wie sieht der Kern von \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q aus?] Ein Polynom \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ist offenbar genau dann im von \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q Kern, wenn \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ist.\\E$"} +{"rule":"KLEINSCHREIBUNG_KEIN_NAME","sentence":"^\\QFür den Ring \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q haben wir die Antwort in der Vorlesung „Lineare Algebra“ kennengelernt.\\E$"} +{"rule":"DE_CASE","sentence":"^\\QDer Chinesische Restsatz.\\E$"} +{"rule":"DE_CASE","sentence":"^\\QDer Chinesische Restsatz ist langweilig, darf aber in keiner Vorlesung fehlen und kommt auch in den allermeisten Klausuren und Prüfungen vor.\\E$"} +{"rule":"DE_CASE","sentence":"^\\QWenn \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q sind, dann ist diese notwendige Bedingung automatisch erfüllt, und der Chinesische Restsatz sagt, dass das Gleichungssystem dann auch lösbar ist.\\E$"} +{"rule":"GERMAN_SPELLER_RULE","sentence":"^\\QDann ist der kanonische Ringhomomorphismus \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\QAdd.\\E$"} +{"rule":"GERMAN_SPELLER_RULE","sentence":"^\\Qund Mult.\\E$"} +{"rule":"GERMAN_WORD_REPEAT_BEGINNING_RULE","sentence":"^\\QDer Körper der algebraischen Zahlen, \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ist ein algebraischer Abschluss \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"} +{"rule":"PLURAL_APOSTROPH","sentence":"^\\QIn einem normalen Jahr würde mithilfe von Zorn's Lemma zeigen, dass diese naive Idee tatsächlich trägt.\\E$"} +{"rule":"PLURAL_APOSTROPH","sentence":"^\\QZorn's Lemma = eine Variante des Auswahlaxioms\\E$"} +{"rule":"DOPPELTE_SATZZEICHEN","sentence":"^\\QWorum geht es in diesem Teil der Vorlesung?.\\E$"} +{"rule":"GERMAN_SPELLER_RULE","sentence":"^\\QEin wichtiges Problem der Algebra(klausur/prüfung) ist es, zu einem gegebenen Körper \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q und zu einem gegebenen Polynom \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q den Zerfällungskörper zu bestimmen.\\E$"} +{"rule":"GERMAN_SPELLER_RULE","sentence":"^\\QWir erhalten also einen Gruppenmorphismus \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q-isomorphismen \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\QPermutationen der Menge \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q.\\E$"} +{"rule":"GERMAN_SPELLER_RULE","sentence":"^\\QWenn alles 100%ig korrekt sein sollte, müsste ich an dieser könnte den Polynomring ausführlich mithilfe einer universellen Eigenschaft definieren.\\E$"} +{"rule":"GERMAN_SPELLER_RULE","sentence":"^\\QWenn alles 100%ig korrekt sein sollte, müsste ich an dieser Stelle den Polynomring ausführlich mithilfe einer universellen Eigenschaft definieren.\\E$"} +{"rule":"GERMAN_SPELLER_RULE","sentence":"^\\QDie Sätze klären auch noch einmal, warum SAGE eckige Klammern verwendet und den Körper „\\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q adjungiert \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q“ mit QQ[sqrt(5)] bezeichnet.\\E$"} +{"rule":"KOMMA_ZWISCHEN_HAUPT_UND_NEBENSATZ","sentence":"^\\QFür beliebige Körpererweiterungen \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q und beliebige Teilmengen \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q ist die Äquivalenz \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q alle \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q sind algebraisch ganz falsch.\\E$"} +{"rule":"DOPPELTES_AUSRUFEZEICHEN","sentence":"^\\QFalsch!!\\E$"} +{"rule":"DE_CASE","sentence":"^\\QDann ist \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q Ist mir zu langweilig.\\E$"} diff --git a/06.tex b/06.tex index 85ad969..d107ff8 100644 --- a/06.tex +++ b/06.tex @@ -30,20 +30,20 @@ Quotientenkörper. Integritätsring an. \end{obs} -Die folgende Definition klärt ganz präzise, was wir mit einem ``möglichst -kleinen Körper, der $R$ enthält'' eigentlich genau meinen. Wenn Sie bei mir die -Vorlesung ``Lineare Algebra'' gehört haben, dann wird Ihnen die folgende +Die folgende Definition klärt ganz präzise, was wir mit einem „möglichst kleinen +Körper, der $R$ enthält“ eigentlich genau meinen. Wenn Sie bei mir die +Vorlesung „Lineare Algebra“ gehört haben, dann wird Ihnen die folgende Definition sehr vertraut vorkommen. Falls nicht, ist jetzt die perfekte -Gelegenheit, alles über ``universelle Eigenschaften'' zu lernen. +Gelegenheit, alles über „universelle Eigenschaften“ zu lernen. \begin{definition}[Quotientenkörper] Sei $R$ ein Integritätsring. Ein \emph{Quotientenkörper von - $R$}\index{Quotientenkörper} ist ein Körper $K$ zusammen mit einem - injektiven Ringhomomorphismus $ι : R → K$, sodass folgende universelle - Eigenschaft gilt: Ist $j : R → L$ ein weiterer injektiver Ringhomomorphismus - von $R$ in einem Körper $L$, dann existiert genau ein Ringhomomorphismus - $h:K→ L$, sodass $j=h◦ i$ ist. Mit anderen Worten, es existiert genau ein - Ringhomomorphismus, sodass das folgende Diagramm kommutiert, + $R$}\index{Quotientenkörper} ist ein Körper $K$ zusammen mit einem injektiven + Ringhomomorphismus $ι : R → K$, sodass folgende universelle Eigenschaft gilt: + Ist $j : R → L$ ein weiterer injektiver Ringhomomorphismus von $R$ in einem + Körper $L$, dann existiert genau ein Ringhomomorphismus $h:K→ L$, sodass $j=h◦ + i$ ist. Mit anderen Worten, es existiert genau ein Ringhomomorphismus, sodass + das folgende Diagramm kommutiert, \[ \begin{tikzcd} R \ar[r, hook, "ι"] \ar[d, equals] & K \ar[d, "∃ ! h"] \\ @@ -93,15 +93,15 @@ Quotientenkörpers. Den folgenden Beweis sollten Sie genau verstehen! \end{proof} Der Witz ist, dass die Abbildung $h$ aus Satz~\ref{satz:edvq} eindeutig gegeben -ist. Die Aussage ``es existiert eine eindeutiger Morphismus'' ist eine viel -bessere Aussage als ``es existiert irgendein Morphismus (dessen Konstruktion -vielleicht von irgendwelchen Wahlen abhängt, die ich treffen muss)''. Das ist -super-wichtig! Man sagt, ``Quotientenkörper sind eindeutig bis auf kanonische -Isomorphie''. +ist. Die Aussage „es existiert eine eindeutiger Morphismus“ ist eine viel +bessere Aussage als „es existiert irgendein Morphismus (dessen Konstruktion +vielleicht von irgendwelchen Wahlen abhängt, die ich treffen muss)“. Das ist +super-wichtig! Man sagt, „Quotientenkörper sind eindeutig bis auf kanonische +Isomorphie“. \begin{notation} Obwohl Quotientenkörper nur bis auf kanonische Isomorphie eindeutig sind, - spricht man oft von ``dem'' Quotientenkörper. Die Notation $Q(R)$ ist üblich. + spricht man oft von „dem“ Quotientenkörper. Die Notation $Q(R)$ ist üblich. \end{notation} \begin{satz}[Existenz von Quotientenkörpern] diff --git a/07.tex b/07.tex index ac8dd9a..993ba24 100644 --- a/07.tex +++ b/07.tex @@ -12,8 +12,8 @@ ist. Für Polynome $f ∈ ℚ[x]$ werden wir die Frage nach der Irreduzibilität vollständig beantworten. Wir erinnern uns daran, wie die Frage nach der -Konstruierbarkeit der ``Verdoppelung des Würfels'' mit der Frage zusammenhing, -ob das Polynom $x³-2 ∈ ℚ[x]$ irreduzibel ist. +Konstruierbarkeit der „Verdoppelung des Würfels“ mit der Frage zusammenhing, ob +das Polynom $x³-2 ∈ ℚ[x]$ irreduzibel ist. \begin{beobachtung} Im Ring $ℤ[x]$ sind Teilbarkeitsfragen oft durch Teilbarkeitsbetrachtungen der @@ -40,7 +40,7 @@ ob das Polynom $x³-2 ∈ ℚ[x]$ irreduzibel ist. Das folgende Irreduzibilitätskriterium von Gauß\index{Irreduzibilitätskriterium von Gauß} zeigt, dass $x³-2$ dann auch irreduzibel in $ℚ[x]$ ist! -\begin{satz}[Irreduzibilitätskriterium von Gauß]\label{satz:Irreduzibilitaetssatz_Gaus} +\begin{satz}[Irreduzibilitätskriterium von Gauß]\label{satz:Irreduzibilitaetssatz_Gaus}% Es sei $R$ ein faktorieller Ring, es sei $K=Q(R)$ sein Quotientenkörper und es sei ein Polynom $f ∈ R[x]$ von positivem Grad gegeben. Wenn $f$ in $R[x]$ irreduzibel ist, dann ist $f$ auch in $K[x]$ irreduzibel. @@ -49,18 +49,18 @@ Das folgende Irreduzibilitätskriterium von Gauß\index{Irreduzibilitätskriteri Als Vorbereitung zum Beweis zeigen wir erst einmal das folgende Lemma. Das Lemma zeigt auch, wie natürlich das Kriterium von Gauß ist. -\begin{lemma}\label{Lemma_zu_Irreduzibilitaetssatz} - Sei $R$ ein faktorieller Ring, es sei $K = Q(R)$ der Quotientenkörper und - $g ∈ K[x] ∖ \{0\}$ sei ein Polynom. Dann existiert ein $a∈ K∖ \{0\}$, sodass - $a· g$ in $R[x]$ ist und sodass der $\ggT$ der Koeffizienten von $a· g$ gleich - $1$ ist. +\begin{lemma}\label{Lemma_zu_Irreduzibilitaetssatz}% + Sei $R$ ein faktorieller Ring, es sei $K = Q(R)$ der Quotientenkörper und $g ∈ + K[x] ∖ \{0\}$ sei ein Polynom. Dann existiert ein $a∈ K∖ \{0\}$, sodass $a· + g$ in $R[x]$ ist und sodass der $\ggT$ der Koeffizienten von $a· g$ gleich $1$ + ist. \end{lemma} \begin{bemerkung} Wir hatten nur den $\ggT$ für zwei Elemente definiert, die Definition geht - genau so für mehr als zwei Elemente. Für Polynome - $a_0 + a_1·x + ⋯ + a_m·x^m ∈ R[x]$ ist die Bedingung $\ggT(a_0, …, a_m) = 1$ - notwendig, aber nicht hinreichend für die Irreduzibilität. + genau so für mehr als zwei Elemente. Für Polynome $a_0 + a_1·x + ⋯ + a_m·x^m + ∈ R[x]$ ist die Bedingung $\ggT(a_0, …, a_m) = 1$ notwendig, aber nicht + hinreichend für die Irreduzibilität. \end{bemerkung} \begin{proof}[Beweis von Lemma~\ref{Lemma_zu_Irreduzibilitaetssatz}] @@ -81,7 +81,7 @@ in endlich vielen Rechenschritten entscheiden ($→$Klausur). Ein Verfahren sol jetzt ganz kurz skizziert werden. Den folgenden Satz kennen Sie vielleicht aus den Anfängervorlesungen. -\begin{erinnerung}[Lagrangesche Interpolationsformel\footnote{\href{https://de.wikipedia.org/wiki/Joseph-Louis_Lagrange}{Joseph-Louis de Lagrange} (* 25. Januar 1736 in Turin als Giuseppe Lodovico Lagrangia; † 10. April 1813 in Paris) war ein italienischer Mathematiker und Astronom.}\index{Lagrangesche Interpolationsformel}] +\begin{erinnerung}[Lagrangesche Interpolationsformel\footnote{\href{https://de.wikipedia.org/wiki/Joseph-Louis_Lagrange}{Joseph-Louis de Lagrange} (* 25.~Januar 1736 in Turin als Giuseppe Lodovico Lagrangia; † 10.~April 1813 in Paris) war ein italienischer Mathematiker und Astronom.}\index{Lagrangesche Interpolationsformel}]% Es sei $K$ ein Körper\footnote{Wir denken an $K = ℚ$.}, es sei $f(x) ∈ K[x]$ ein Polynom vom Grad $≤ n$ und es seien $a_1, …, a_{n+1}∈ K$ paarweise verschiedene Elemente. Dann ist $f$ durch seine Werte $f(a_1), …, f(a_{n+1})$ @@ -137,16 +137,16 @@ Frage nach der Irreduzibilität zwar beantworten, allerdings sind die nötigen Rechnungen ziemlich aufwändig (besonders bei Zeitdruck in einer Klausur!). Das folgende Kriterium von Theodor Schönemann\footnote{\href{https://de.wikipedia.org/wiki/Theodor_Sch\%C3\%B6nemann}{Theodor - Schönemann} (* 4. April 1812 in Driesen, Friedebergischer Kreis; † - 16. Januar 1868 in Brandenburg an der Havel) war ein deutscher Mathematiker.}, -das in der Literatur durchgehend falsch mit ``Eisenstein-Kriterium'' +Schönemann} (* 4.~April 1812 in Driesen, Friedebergischer Kreis; † 16.~Januar +1868 in Brandenburg an der Havel) war ein deutscher Mathematiker.}, das in der +Literatur durchgehend falsch mit „Eisenstein-Kriterium“ bezeichnet\footnote{\href{https://de.wikipedia.org/wiki/Gotthold_Eisenstein}{Ferdinand - Gotthold Max Eisenstein} (* 16. April 1823 in Berlin; † 11. Oktober 1852 - ebenda) war ein deutscher Mathematiker, der hauptsächlich in der Zahlentheorie - und über elliptische Funktionen arbeitete.} wird, ist oft viel schneller. Es -ist so wichtig, dass es dazu sogar +Gotthold Max Eisenstein} (* 16.~April 1823 in Berlin; † 11.~Oktober 1852 ebenda) +war ein deutscher Mathematiker, der hauptsächlich in der Zahlentheorie und über +elliptische Funktionen arbeitete.} wird, ist oft viel schneller. Es ist so +wichtig, dass es dazu sogar \href{https://de.wikipedia.org/wiki/Eisensteinkriterium}{eine eigene Seite auf - Wikipedia} gibt\index{Eisenstein-Kriterium}. +Wikipedia} gibt\index{Eisenstein-Kriterium}. \begin{satz}[Eisenstein Kriterium]\label{Satz_Eisenstein_Kriterium} Es sei $R$ ein faktorieller Ring und es sei @@ -182,8 +182,8 @@ ist so wichtig, dass es dazu sogar \begin{equation*} x_1^m+g(x_2, …, x_n) ∈ R[x_1, …, x_n] \end{equation*} - über einem faktoriellen Ring $R$ ist sicher dann irreduzibel, wenn $g(x_2, …, x_n) ∈ R[x_2, …, x_n]$ - irreduzibel ist. + über einem faktoriellen Ring $R$ ist sicher dann irreduzibel, wenn $g(x_2, …, + x_n) ∈ R[x_2, …, x_n]$ irreduzibel ist. \end{bsp} @@ -201,10 +201,10 @@ einen Ringmorphismus zu betrachten und folgendes Lemma anzuwenden. jetzt $\varphi(f) ∈ S$ irreduzibel ist, dann ist auch $f∈ R[x]$ irreduzibel. \end{lem} \begin{proof} - Angenommen, $f$ wäre reduzibel. Dann können wir schreiben $f = g·h$, wobei $g$ - und $h$ jeweils keine Einheiten in $R[x]$ sind. Weil der größte gemeinsame - Teiler der Koeffizienten gleich $1$ ist, müssen $g$ und $h$ jeweils positiven - Grad haben. Die Gleichung + Angenommen, $f$ wäre reduzibel. Dann können wir schreiben $f = g·h$, wobei + $g$ und $h$ jeweils keine Einheiten in $R[x]$ sind. Weil der größte + gemeinsame Teiler der Koeffizienten gleich $1$ ist, müssen $g$ und $h$ jeweils + positiven Grad haben. Die Gleichung \begin{equation*} \varphi(f) = \varphi(g)·\varphi(h) \end{equation*} @@ -214,20 +214,20 @@ einen Ringmorphismus zu betrachten und folgendes Lemma anzuwenden. Ringmorphismen, die man in der Praxis brauchen kann, entstehen oft auf die folgenden Weisen. \begin{description} -\item[Anwenden eines Ringhomomorphismus auf die Koeffizienten:] Ist +\item[Anwenden eines Ringhomomorphismus auf die Koeffizienten] Ist $\varphi : R → S$ ein Ringhomomorphismus, dann ist auch \begin{equation*} Φ: R[x] → S[x], \quad \sum a_{ν} x^ν ↦ \sum\varphi(a_{ν})x^ν \end{equation*} ein Ringmorphismus. -\item[Einsetzungskomposition:]\index{Einsetzungskomposition} Es sei eine +\item[Einsetzungskomposition]\index{Einsetzungskomposition} Es sei eine Abbildung $\varphi : R → S$ und es sei ein Element $t ∈ S$ gegeben. Setze \begin{equation*} Φ : R[x] → S, \quad \sum a_{ν} x^ν ↦ \sum\varphi(a_{ν})t^ν \end{equation*} -\item[Substitutionsmorphismus:]\index{Substitutionsmorphismus} Es sei ein +\item[Substitutionsmorphismus]\index{Substitutionsmorphismus} Es sei ein Element $a∈ R$ gegeben. Dann betrachte die Abbildung \begin{equation*} Φ : R[x] → R[x], \quad \sum a_{ν} x^ν ↦ \sum a_{ν}(x-a)^ν. diff --git a/08.tex b/08.tex index 9b50a7c..f17a1ad 100644 --- a/08.tex +++ b/08.tex @@ -17,8 +17,8 @@ Debatte war. Der nächste Satz stellt die Verbindung zwischen Körpertheorie und Konstruierbarkeit her. Die Formulierung des Satzes verwendet den Begriff -``konjugierte Menge''. Dabei ist ``konjugiert'' wie immer nur eine bombastische -Formulierung für ``an der reellen Achse gespiegelt''. +„konjugierte Menge“. Dabei ist „konjugiert“ wie immer nur eine bombastische +Formulierung für „an der reellen Achse gespiegelt“. \begin{notation}[Konjungierte Menge] Es sei $M ⊂ ℂ$ eine Menge. Dann betrachte die Menge @@ -29,14 +29,13 @@ Formulierung für ``an der reellen Achse gespiegelt''. \begin{rem} Im Fall, wo die Menge $M$ die Elemente $0$ und $1$ enthält, kann man die Spiegelung an der reellen Achse mit Zirkel und Lineal konstruieren. Damit ist - klar, dass $\overline{M} ⊂ \Kons(M)$ ist. Es ist in diesem Fall auch - klar, dass $i ∈ \Kons(M)$ ist. + klar, dass $\overline{M} ⊂ \Kons(M)$ ist. Es ist in diesem Fall auch klar, + dass $i ∈ \Kons(M)$ ist. \end{rem} -\begin{satz}[Hausaufgabe Blatt 2, Aufgabe 3]\label{Satz_von_Seite_69} - Es sei $\{0,1 \} ⊂ M ⊂ ℂ$ und es sei $z ∈ \Kons(M)$. Sei weiter - $K = ℚ(M ∪ \overline{M})$. Dann existiert eine Zahl $k ∈ ℕ$, sodass die - Gleichheit +\begin{satz}[Hausaufgabe Blatt 2, Aufgabe 3]\label{Satz_von_Seite_69}% + Es sei $\{0,1 \} ⊂ M ⊂ ℂ$ und es sei $z ∈ \Kons(M)$. Sei weiter $K = ℚ(M ∪ + \overline{M})$. Dann existiert eine Zahl $k ∈ ℕ$, sodass die Gleichheit \begin{equation*} [K(z) : K] = 2^k \end{equation*} @@ -47,9 +46,8 @@ Formulierung für ``an der reellen Achse gespiegelt''. \section{Verdopplung des Würfels} -Das klassische Konstruktionsproblem ``Verdopplung des Würfels'' ist mit Zirkel -und Lineal nicht möglich, denn mit $M := \{0,1\}$ ist -$ℚ = ℚ(M ∪ \overline{M})$ und +Das klassische Konstruktionsproblem „Verdopplung des Würfels“ ist mit Zirkel und +Lineal nicht möglich, denn mit $M := \{0,1\}$ ist $ℚ = ℚ(M ∪ \overline{M})$ und \[ [ℚ(\sqrt[3]{2}): ℚ ] = 3, \] @@ -62,11 +60,11 @@ $\sqrt[3]{2}$ ist. Bevor wir die Frage nach der Dreiteilung des Winkel abschließend beantworten, beweise ich zuerst ein Satz, der auch später noch von Interesse sein wird. -\begin{satz}\label{Satz_Vor_Dreiteilung_Zirkel_Lineal} +\begin{satz}\label{Satz_Vor_Dreiteilung_Zirkel_Lineal}% Es sei $L/K$ eine Körpererweiterung und es sei $a ∈ L$ ein über $K$ transzendentes Element. Dann ist $K(a)$ isomorph zum Körper der gebrochen-rationalen Funktionen\footnote{Siehe Beispiel~\ref{bsp:2-3-3} im - Falle $K = ℝ$.} über $K$ in einer Variablen. Mit anderen Worten: + Falle $K = ℝ$.} über $K$ in einer Variablen. Mit anderen Worten: \begin{equation*} K(a) ≅ K(x) = Q(K[x]) \end{equation*} @@ -77,11 +75,11 @@ beweise ich zuerst ein Satz, der auch später noch von Interesse sein wird. Damit lässt sich die Konstruierbarkeitsfrage ganz gut beantworten. -\begin{satz}\label{Satz_Dreiteilung_Zirkel_Lineal} +\begin{satz}\label{Satz_Dreiteilung_Zirkel_Lineal}% Gegeben sei eine reelle Zahl $\varphi ∈ (0, 2·π)$. Falls $e^{i\varphi}$ - transzendent ist, dann ist - $e^{(\varphi i)/3} \not ∈ \Kons(\{0,1, e^{\varphi i}\})$. Die Dreiteilung des - Winkels $\varphi$ ist also mit Zirkel und Lineal nicht möglich. + transzendent ist, dann ist $e^{(\varphi i)/3} \not ∈ \Kons(\{0,1, e^{\varphi + i}\})$. Die Dreiteilung des Winkels $\varphi$ ist also mit Zirkel und Lineal + nicht möglich. \end{satz} \begin{proof} \video{9-3} @@ -93,14 +91,14 @@ Damit lässt sich die Konstruierbarkeitsfrage ganz gut beantworten. Konstruktionsverfahren für die Dreiteilung des Winkels. \end{bemerkung} \begin{proof} - Wenn $z=e^{i\varphi}$ algebraisch über $ℚ$ ist, dann ist auch - $\overline{z} = e^{-i\varphi}$ algebraisch über $ℚ$, denn $z$ und - $\overline{z}$ haben beide dasselbe Minimalpolynom. Also ist auch der Realteil + Wenn $z=e^{i\varphi}$ algebraisch über $ℚ$ ist, dann ist auch $\overline{z} = + e^{-i\varphi}$ algebraisch über $ℚ$, denn $z$ und $\overline{z}$ haben beide + dasselbe Minimalpolynom. Also ist auch der Realteil \begin{equation*} \operatorname{Re}(z) =\frac12(z+\overline{z}) \end{equation*} - algebraisch über $ℚ$. Das zeigt, dass die Menge $\varphi∈ (0,2π)$, für - die $e^{i\varphi}$ transzendent ist, in $(0,2π)$ dicht ist. + algebraisch über $ℚ$. Das zeigt, dass die Menge $\varphi∈ (0,2π)$, für die + $e^{i\varphi}$ transzendent ist, in $(0,2π)$ dicht ist. \end{proof} diff --git a/09.tex b/09.tex index c45f841..5164761 100644 --- a/09.tex +++ b/09.tex @@ -4,25 +4,20 @@ \chapter{Ideale} \label{chapt:09} -Für dieses Kapitel haben wir Ihnen Beispiele auf unserem -\href{https://sage.cplx.vm.uni-freiburg.de/share/}{Sage/CoCalc-Server} -bereitgestellt. - - \section{Wohin geht die Reise} Ich hatte schon am Ende des letzten Abschnittes geschrieben: um die Frage nach der Konstruierbarkeit des regelmäßigen $n$-Ecks vollständig entscheiden zu können, müssen wir die Symmetrien von Körpererweiterungen verstehen … und -vielleicht irgendwann auch definieren, was mit ``Symmetrie einer -Körpererweiterung'' gemeint sein soll. All das wird voraussetzen, dass wir +vielleicht irgendwann auch definieren, was mit „Symmetrie einer +Körpererweiterung“ gemeint sein soll. All das wird voraussetzen, dass wir Körpererweiterungen besser beschreiben. Die Idee ist die: gegeben eine einfache, algebraische Erweiterung $K(α)/K$ vom Grad $n$, dann wissen wir schon, dass wir alle Elemente des Oberkörpers $K(α)$ als Linearkombinationen der Form \[ k_0 + k_1·α + k_2·α² + ⋯ k_{n-1}·α^{n-1} \] -schreiben könne, wobei die $k_{•}$ geeignete Elemente des kleineren Körpers $K$ +schreiben könne, wobei die $k_•$ geeignete Elemente des kleineren Körpers $K$ sind. Diese Einsicht ist natürlich extrem hilfreich --- wir kennen das von den komplexen Zahlen, die sich alle in der Form $k_0 + k_1·\sqrt{-1}$ schreiben lassen. Der Sachverhalt lässt sich auch anders formulieren: Der @@ -36,16 +31,16 @@ liegt es dann nahe, den Körper $K(α)$ als Quotient zu beschreiben, K(α) = \factor{K[x]}{\ker φ}. \end{equation} Diese Beschreibung\footnote{\label{foot:sage}Hatten Sie sich gewundert, warum - SAGE eckige Klammern verwendet und den Körper ``$ℚ$ adjungiert $\sqrt{5}$'' - mit \texttt{QQ[sqrt(5)]} bezeichnet? Der Grund ist, das runde Klammern in der - Programmiersprache Python schon eine andere Bedeutung haben. - Gleichung~\eqref{eq:xx} zeigt aber, dass eckige Klammer in dieser Situation - ganz sinnvoll sind.} wird sehr hilfreich sein, denn wir kommen mit dem -vertrauten Polynomring $K[X]$ besser klar als mit dem etwas unheimlichen Körper -$K(α)$. Um alles korrekt zu definieren, müssen wir uns aber erst noch einmal -überlegen, was für eine Art von Objekt $\ker φ$ nun tatsächlich ist, und was -``Quotient'' genau bedeuten soll. Ich nehme die Antwort gleich vorweg: Die -Menge $\ker φ$ ist das typische Beispiel eines ``Ideals im Ring $K[x]$''. +SAGE eckige Klammern verwendet und den Körper „$ℚ$ adjungiert $\sqrt{5}$“ mit +\texttt{QQ[sqrt(5)]} bezeichnet? Der Grund ist, das runde Klammern in der +Programmiersprache Python schon eine andere Bedeutung haben. +Gleichung~\eqref{eq:xx} zeigt aber, dass eckige Klammer in dieser Situation ganz +sinnvoll sind.} wird sehr hilfreich sein, denn wir kommen mit dem vertrauten +Polynomring $K[X]$ besser klar als mit dem etwas unheimlichen Körper $K(α)$. Um +alles korrekt zu definieren, müssen wir uns aber erst noch einmal überlegen, was +für eine Art von Objekt $\ker φ$ nun tatsächlich ist, und was „Quotient“ genau +bedeuten soll. Ich nehme die Antwort gleich vorweg: Die Menge $\ker φ$ ist das +typische Beispiel eines „Ideals im Ring $K[x]$“. \section{Elementare Definitionen} @@ -68,30 +63,30 @@ Die technisch korrekte Definition eines Ideals ist jetzt die folgende. man in der Definition $r·a$ oder $a·r$ schreibt, definiert man ein Links- oder Rechtsideal\index{Linksideal}\index{Rechtsideal}. Ideale, die sowohl Links- als auch Rechtsideale sind, heißen beidseitige Ideale\index{beidseitiges - Ideal}. In kommutativen Ringen, für die wir uns hier interessieren, fallen + Ideal}. In kommutativen Ringen, für die wir uns hier interessieren, fallen diese Begriffe zusammen. \end{bemerkung} \begin{bemerkung} Der Name \emph{Ideal} geht auf Kummer\footnote{\href{https://de.wikipedia.org/wiki/Ernst_Eduard_Kummer}{Ernst - Eduard Kummer} (* 29. Januar 1810 in Sorau, Niederlausitz; † 14. Mai 1893 - in Berlin) war ein deutscher Mathematiker und Hochschullehrer, der sich vor - allem mit Zahlentheorie, Analysis und Geometrie befasste.} und + Eduard Kummer} (* 29.~Januar 1810 in Sorau, Niederlausitz; † 14.~Mai 1893 in + Berlin) war ein deutscher Mathematiker und Hochschullehrer, der sich vor allem + mit Zahlentheorie, Analysis und Geometrie befasste.} und Dedekind\footnote{\href{https://de.wikipedia.org/wiki/Richard_Dedekind}{Julius - Wilhelm Richard Dedekind} (* 6. Oktober 1831 in Braunschweig; † - 12. Februar 1916 ebenda) war ein deutscher Mathematiker.} zurück. Kummer - hatte bei der Untersuchung der Teilbarkeit in gewissen nicht-faktoriellen - Ringen wie $ℤ[\sqrt{-5}]$ gewisse \emph{ideale Zahlen} eingeführt. Dedekind - hat dann den Idealbegriff geprägt. + Wilhelm Richard Dedekind} (* 6.~Oktober 1831 in Braunschweig; † 12.~Februar + 1916 ebenda) war ein deutscher Mathematiker.} zurück. Kummer hatte bei der + Untersuchung der Teilbarkeit in gewissen nicht-faktoriellen Ringen wie + $ℤ[\sqrt{-5}]$ gewisse \emph{ideale Zahlen} eingeführt. Dedekind hat dann den + Idealbegriff geprägt. \end{bemerkung} \begin{bsp}[Triviale Ideale] In jedem kommutativen Ring $R$ sind $I= \{0\}$ und $I=R$ trivialerweise Ideale. Wenn $R$ ein Körper ist, dann sind das auch die einzigen Ideale. Grund: wenn $R$ ein Körper und $I ⊂ R$ ein Ideal ist und $a ∈ I∖ \{0\}$, dann - ist auch jedes andere Körperelement in $I$. Sei nämlich irgendein Element - $r ∈ R$ gegeben. Nach Definition~\ref{def:ideal} ist + ist auch jedes andere Körperelement in $I$. Sei nämlich irgendein Element $r + ∈ R$ gegeben. Nach Definition~\ref{def:ideal} ist \[ r = (r·a^{-1})·a ∈ I. \] @@ -120,7 +115,7 @@ Die technisch korrekte Definition eines Ideals ist jetzt die folgende. Sie ein Programm, um mit diesen Kurven zu spielen. Sie können das Programm auch \href{https://cplx.vm.uni-freiburg.de/storage/software/ellipticcurve/wasm/ellipticcurve.html}{direkt - im Browser laufen lassen}. Abbildung Public Domain aus + im Browser laufen lassen}. Abbildung Public Domain aus \href{https://en.wikipedia.org/wiki/Crunode#/media/File:Cubic_with_double_point.svg}{Wikipedia}. \caption{Knotenkurve} \label{fig:node} @@ -153,10 +148,10 @@ Die technisch korrekte Definition eines Ideals ist jetzt die folgende. V= \{ \vec{x} ∈ K^n \::\: f_1(\vec{x}) = ⋯ = f_n(\vec{x})=0 \} \] wobei $f_i ∈ K[x_1, …, x_n]$ irgendwelche Polynome sind. Man nennt ein - solches $V$ manchmal \emph{algebraische Varietät}\index{algebraische Varietät}. - Abbildung~\ref{fig:node} zeigt ein Beispiel. Im Internet finden Sie - \href{https://imaginary.org/gallery/surfer-gallery-by-bianca-violet}{hier} und - \href{https://imaginary.org/gallery/oliver-labs}{hier} noch weitere schöne + solches $V$ manchmal \emph{algebraische Varietät}\index{algebraische + Varietät}. Abbildung~\ref{fig:node} zeigt ein Beispiel. Im Internet finden + Sie \href{https://imaginary.org/gallery/surfer-gallery-by-bianca-violet}{hier} + und \href{https://imaginary.org/gallery/oliver-labs}{hier} noch weitere schöne Beispiele. Definiere dann das Ideal @@ -170,7 +165,7 @@ Die technisch korrekte Definition eines Ideals ist jetzt die folgende. In der \emph{Algebraischen Geometrie}, dem Gebiet auf dem ich und meine Mitarbeiter arbeiten, geht es darum, geometrische Räume mithilfe von algebraischen Objekten wie etwa Idealen zu beschreiben. Tatsächlich lässt sich -ein fast vollständiges Wörterbuch ``Algebra $\leftrightarrow$ Geometrie'' +ein fast vollständiges Wörterbuch „Algebra $\leftrightarrow$ Geometrie“ aufstellen. @@ -179,8 +174,8 @@ aufstellen. \sideremark{Vorlesung 10}Es gibt noch eine andere, ganz wichtige Klasse von Beispielen, die wir in ähnlicher Form schon aus der linearen Algebra kennen. Gegeben einen $K$-Vektorraum $V$ und eine beliebige Teilmenge $M ⊂ V$, so -betrachteten wir in der linearen Algebra den ``von $M$ erzeugten -Untervektorraum'' und bezeichneten diesen Raum mit $\langle M \rangle_K$ oder +betrachteten wir in der linearen Algebra den „von $M$ erzeugten Untervektorraum“ +und bezeichneten diesen Raum mit $\langle M \rangle_K$ oder $\operatorname{Span}(M)$. Per Definition gilt: Ein Vektor $\vec{v} ∈ V$ liegt genau dann in $\langle M \rangle_K$, wenn $\vec{v}$ sich als Linearkombination der Elemente von $M$ schreiben lässt. Wenn die Menge $M$ unendlich ist, was @@ -226,22 +221,22 @@ Ideale sind die, die mithilfe eines einzigen Erzeugers definiert werden können. Dann gilt offensichtlich \begin{align*} (a_1) ⊂ (a_2) & ⇔ a_2| a_1 \\ - (a_1) = (a_2)& ⇔ a_1 \sim a_2 + (a_1) = (a_2)& ⇔ a_1 \sim a_2. \end{align*} Die Hauptideale in $R$ entsprechen also eindeutig Klassen von zueinander assoziierten Elementen. \end{beobachtung} \begin{warnung} - Im Gegensatz zu Vektorräumen gibt es für Ideale keinen ``Basisaustauschsatz'', + Im Gegensatz zu Vektorräumen gibt es für Ideale keinen „Basisaustauschsatz“, denn zum Beweis des Basisaustauschsatzes ist es absolut notwendig zu dividieren! Es ist nicht immer richtig, dass zwei minimale Erzeugendensysteme eines Ideals, \[ I = (a_1, …, a_n) = (b_1, …, b_m), \] - immer gleiche Mächtigkeit haben. Falls sie vorhatten, die ``Dimension'' eines - Ideals zu definieren -- nice try! + immer gleiche Mächtigkeit haben. Falls sie vorhatten, die „Dimension“ eines + Ideals zu definieren -- \foreignlanguage{english}{Nice try}! \end{warnung} Ein Ideal ist in der Praxis nur dann handhabbar, wenn ich eine möglichst @@ -345,35 +340,33 @@ Satz sollte ihnen bekannt vorkommen. Angenommen, es gäbe eine nicht-leere Menge $M$ von Idealen aus $R$ ohne maximales Element. Dann gibt es zu jedem $I_0∈ M$ ein $I_1∈ M$ mit $I_0\subsetneqq I_1$, genau so mit $I_2,I_3,\dots$. Wir erhalten einen - Widerspruch zur Annahme, dass der ``Teilerkettensatz für Ideale'' gilt. + Widerspruch zur Annahme, dass der „Teilerkettensatz für Ideale“ gilt. - \item[\ref{Satz_Ideale_aequiv_3}$⇒$\ref{Satz_Ideale_aequiv_1}] Sei - $I⊂ R$ ein Ideal und $M$ die Menge aller Ideale $J⊂ R$, die endlich erzeugt - und in $I$ enthalten sind. Dann ist $M$ nicht leer, denn $(0) ∈ M$. Also - gibt es per Annahme ein maximales Element $J∈ M$. Nach Annahme ist $J$ - endlich erzeugt, also $J = (a_1, …, a_n)$ und wir müssen zeigen, dass - $J = I$ ist. Wenn es aber ein $b ∈ I∖J$ gäbe, dann wäre - $(a_1, …, a_n,b) ∈ M$ ein Ideal, das $J$ enthält. Ein Widerspruch zur - Annahme. \qedhere + \item[\ref{Satz_Ideale_aequiv_3}$⇒$\ref{Satz_Ideale_aequiv_1}] Sei $I⊂ R$ ein + Ideal und $M$ die Menge aller Ideale $J⊂ R$, die endlich erzeugt und in $I$ + enthalten sind. Dann ist $M$ nicht leer, denn $(0) ∈ M$. Also gibt es per + Annahme ein maximales Element $J∈ M$. Nach Annahme ist $J$ endlich erzeugt, + also $J = (a_1, …, a_n)$ und wir müssen zeigen, dass $J = I$ ist. Wenn es + aber ein $b ∈ I∖J$ gäbe, dann wäre $(a_1, …, a_n,b) ∈ M$ ein Ideal, das $J$ + enthält. Ein Widerspruch zur Annahme. \qedhere \end{description} \end{proof} Der folgende Satz von David Hilbert\footnote{\href{https://de.wikipedia.org/wiki/David_Hilbert}{David - Hilbert} (* 23. Januar 1862 in Königsberg; † 14. Februar 1943 in - Göttingen) war ein deutscher Mathematiker. Er gilt als einer der - bedeutendsten Mathematiker der Neuzeit. Viele seiner Arbeiten auf dem Gebiet - der Mathematik und mathematischen Physik begründeten eigenständige - Forschungsgebiete. Mit seinen Vorschlägen begründete er die bis heute - bedeutsame formalistische Auffassung von den Grundlagen der Mathematik und - veranlasste eine kritische Analyse der Begriffsdefinitionen der Mathematik und - des mathematischen Beweises. Diese Analysen führten zum Gödelschen - Unvollständigkeitssatz, der unter anderem zeigt, dass das Hilbertprogramm, die - von ihm angestrebte vollständige Axiomatisierung der Mathematik, nicht - gänzlich erfüllt werden kann. Hilberts programmatische Rede auf dem - internationalen Mathematikerkongress in Paris im Jahre 1900, in der er eine - Liste von 23 mathematischen Problemen vorstellte, beeinflusste die - mathematische Forschung des 20. Jahrhunderts nachhaltig.} ähnelt formell dem +Hilbert} (* 23.~Januar 1862 in Königsberg; † 14.~Februar 1943 in Göttingen) war +ein deutscher Mathematiker. Er gilt als einer der bedeutendsten Mathematiker +der Neuzeit. Viele seiner Arbeiten auf dem Gebiet der Mathematik und +mathematischen Physik begründeten eigenständige Forschungsgebiete. Mit seinen +Vorschlägen begründete er die bis heute bedeutsame formalistische Auffassung von +den Grundlagen der Mathematik und veranlasste eine kritische Analyse der +Begriffsdefinitionen der Mathematik und des mathematischen Beweises. Diese +Analysen führten zum Gödelschen Unvollständigkeitssatz, der unter anderem zeigt, +dass das Hilbertprogramm, die von ihm angestrebte vollständige Axiomatisierung +der Mathematik, nicht gänzlich erfüllt werden kann. Hilberts programmatische +Rede auf dem internationalen Mathematikerkongress in Paris im Jahre 1900, in der +er eine Liste von 23 mathematischen Problemen vorstellte, beeinflusste die +mathematische Forschung des 20. Jahrhunderts nachhaltig.} ähnelt formell dem Satz~\ref{Satz_Satz_von_Gauss} von Gauß und ist mindestens genauso wichtig. Historisch war der Satz ein Meilenstein. Hilbert's Beweis erregte auch deshalb großes Aufsehen, weil die Existenz eines endlichen Erzeugendensystems mithilfe diff --git a/10.tex b/10.tex index 63cac00..0da10a8 100644 --- a/10.tex +++ b/10.tex @@ -11,17 +11,17 @@ Ich hatte am Anfang von Kapitel~\ref{chapt:09} schon gesagt, warum wir uns für Ideale interessieren: Wir wollen --ähnlich wie bei der Konstruktion des Quotientenvektoraumes in der Linearen Algebra-- einen Quotienten von Ringen konstruieren. Ich weiß aus Erfahrung, dass viele Studierende ihre Probleme mit -``Quotientenvektorräumen'' haben und nutze an dieser Stelle normalerweise die +„Quotientenvektorräumen“ haben und nutze an dieser Stelle normalerweise die Gelegenheit, um mit der Konstruktion des Restklassenringes die Begriffe und Beweistechniken noch einmal zu wiederholen. In diesem Semester geht das nicht, denn das Semester ist deutlich kürzer als in normalen Jahren. Ich verzichte -deshalb im Folgenden sehr oft auf Beweise und behaupte, dass ``alles genau so -geht, wie in der Linearen Algebra''. +deshalb im Folgenden sehr oft auf Beweise und behaupte, dass „alles genau so +geht, wie in der Linearen Algebra“. \begin{warnung} - Stellen Sie sicher, dass sie sich noch ausreichend gut an die VL ``Lineare - Algebra'' erinnern. Beweisen Sie zur Probe einige Aussagen selbst -- solche - Sachen werden gern in Klausuren und mündlichen Prüfungen gefragt. + Stellen Sie sicher, dass sie sich noch ausreichend gut an die Vorlesung + „Lineare Algebra“ erinnern. Beweisen Sie zur Probe einige Aussagen selbst -- + solche Sachen werden gern in Klausuren und mündlichen Prüfungen gefragt. \end{warnung} @@ -48,8 +48,8 @@ durch folgende universelle Eigenschaft definiert. Wie üblich folgt aus der universellen Eigenschaft, dass Restklassenringen (wenn Sie denn existieren) eindeutig sind bis auf eine eindeutige Isomorphie. Man -spricht deswegen oft nicht ganz richtig von ``dem'' Restklassenring und -bezeichnet ``den'' Restklassenring mit $R/I$. +spricht deswegen oft nicht ganz richtig von „dem“ Restklassenring und bezeichnet +„den“ Restklassenring mit $R/I$. \section{Konstruktion von Restklassenringen} @@ -60,17 +60,17 @@ universellen Eigenschaft -- mit einer Ausnahme: Existenz. Wir beweisen die Existenz wie immer nicht abstrakt, sondern indem wir eine konkrete Konstruktion eines Restklassenringes angeben. -\begin{defn}[Kongruenz modulo Ideal]\label{def:kmi} +\begin{defn}[Kongruenz modulo Ideal]\label{def:kmi}% Es sei $R$ ein kommutativer Ring mit Eins und es sei $I ⊂ R$ ein Ideal. Zwei Elemente $a,b∈ R$ heißen \emph{kongruent modulo $I$}\index{Kongruenz modulo - Ideal}, wenn $a-b ∈ I$ ist. In diesem Fall ist die Schreibweise - $a \equiv b \:\:(\operatorname{mod} I)$ üblich. + Ideal}, wenn $a-b ∈ I$ ist. In diesem Fall ist die Schreibweise $a \equiv b + \:\:(\operatorname{mod} I)$ üblich. \end{defn} -\begin{lem}\label{lem:10-1-2} +\begin{lem}\label{lem:10-1-2}% In der Situation von Definition~\ref{def:kmi} gilt: Kongruenz modulo $I$ ist eine Äquivalenzrelation auf $R$. Für ein gegebenes Element $a ∈ R$ ist die - die Äquivalenzklasse eines gegebenen Elementes $a ∈ R$ ist + Äquivalenzklasse eines gegebenen Elementes $a ∈ R$ ist \begin{equation*} a+I = \{ a+b \::\: b∈ I \} \eqno\qed \end{equation*} @@ -82,22 +82,21 @@ eines Restklassenringes angeben. \end{notation} \begin{bsp} - Der Name ``Restklasse'' kommt von folgendem Beispiel. Sei $R = ℤ$, sei - $m ∈ ℕ$ eine Zahl, und sei $I = (m)$. Dann ist - $a \equiv b \:\:(\operatorname{mod} I)$ genau dann, wenn $a$ und $b$ bei der - Division durch $m$ denselben Rest haben. Die Kongruenz modulo $(m)$ zerlegt - $ℤ$ also genau in die Restklassen + Der Name „Restklasse“ kommt von folgendem Beispiel. Sei $R = ℤ$, sei $m ∈ ℕ$ + eine Zahl, und sei $I = (m)$. Dann ist $a \equiv b \:\:(\operatorname{mod} + I)$ genau dann, wenn $a$ und $b$ bei der Division durch $m$ denselben Rest + haben. Die Kongruenz modulo $(m)$ zerlegt $ℤ$ also genau in die Restklassen \begin{equation*} 0 + (m), 1+(m), 2+(m), …, m-1+(m). \end{equation*} \end{bsp} -\begin{satz}[Existenz von Restklassenringen]\label{satz:exvrklr} +\begin{satz}[Existenz von Restklassenringen]\label{satz:exvrklr}% Sei $R$ ein kommutativer Ring mit Eins und es sei $I⊂ R$ ein Ideal. Die - Äquivalenzrelation ``Kongruenz modulo $I$'' werde mit $\sim$ bezeichnet. Dann + Äquivalenzrelation „Kongruenz modulo $I$“ werde mit $\sim$ bezeichnet. Dann sind die folgenden Verknüpfungen es auf dem Quotienten\footnote{Erinnerung an - die Lineare Algebra: Quotient nach Äquivalenzrelation = $R/\sim$ = Menge der - Äquivalenzklassen} $S := R/\sim$ wohldefiniert: + die Lineare Algebra: Quotient nach Äquivalenzrelation = $R/\sim$ = Menge der + Äquivalenzklassen} $S := R/\sim$ wohldefiniert: \[ \begin{matrix} + : & S ⨯ S & → & S \\ @@ -129,8 +128,8 @@ diese Art und Weise direkt beschreiben. \begin{equation*} \bigl(g_1+(f)\bigr)· \bigl(g_2+(f)\bigr) = h + (f) \end{equation*} - wobei $h$ der Rest von $g_1· g_2$ bei der Division durch $f$ ist. Ist - $\deg f ≥ 1$, dann ist die Abbildung + wobei $h$ der Rest von $g_1· g_2$ bei der Division durch $f$ ist. Ist $\deg f + ≥ 1$, dann ist die Abbildung \begin{equation*} K → \factor{K[x]}{(f)}, \quad λ ↦ λ+(f) \end{equation*} @@ -144,7 +143,7 @@ diese Art und Weise direkt beschreiben. Der folgende Satz folgt wie in der Linearen Algebra aus der universellen Eigenschaft. -\begin{prop}[Homomorphiesatz für Ringe]\label{Korollar_Homomorphiesatz} +\begin{prop}[Homomorphiesatz für Ringe]\label{Korollar_Homomorphiesatz}% Es sei $R$ ein kommutativer Ring mit Eins, und es sei $ψ : R → S$ ein surjektiver Ringmorphismus. Dann ist die induzierte Abbildung \begin{equation*} @@ -181,18 +180,18 @@ zum Restklassenring $K[x]/(f)$ ist. \section{Ideale oben und unten} Neben dem Homomorphiesatz für Ringe gelten noch einige andere Sätze, die wir aus -der linearen Algebra kennen (``Kürzen'' von Untervektorräumen). Um diese Sätze -korrekt zu formulieren, müssen wir erst verstehen, wie ``Ideale in $R$'' und -``Ideale in $R/I$'' zusammenhängen. Der folgende Satz formuliert den -Zusammenhang nicht nur für die Quotientenabbildung $φ : R → R/I$, sondern für -beliebige Ringmorphismen. Kurz gesagt gilt: Urbilder von Idealen sind immer -Ideale. Bilder von Idealen sind zumindest dann Ideale, wenn der Morphismus -surjektiv ist --- dies ist zum Beispiel bei der Quotientenabbildung der Fall. +der linearen Algebra kennen („Kürzen“ von Untervektorräumen). Um diese Sätze +korrekt zu formulieren, müssen wir erst verstehen, wie „Ideale in $R$“ und +„Ideale in $R/I$“ zusammenhängen. Der folgende Satz formuliert den Zusammenhang +nicht nur für die Quotientenabbildung $φ : R → R/I$, sondern für beliebige +Ringmorphismen. Kurz gesagt gilt: Urbilder von Idealen sind immer Ideale. +Bilder von Idealen sind zumindest dann Ideale, wenn der Morphismus surjektiv ist +--- dies ist zum Beispiel bei der Quotientenabbildung der Fall. \begin{satz}[Urbilder von Idealen] - Es sei $\varphi : R → S$ ein Morphismus von kommutativen Ringen mit Eins. - Wenn $I⊂ S$ ein Ideal ist, dann ist die Urbildmenge $\varphi^{-1}(I)$ ein - Ideal in $R$. Ist $\varphi$ zusätzlich surjektiv, dann ist die Zuordnung + Es sei $\varphi : R → S$ ein Morphismus von kommutativen Ringen mit Eins. Wenn + $I⊂ S$ ein Ideal ist, dann ist die Urbildmenge $\varphi^{-1}(I)$ ein Ideal in + $R$. Ist $\varphi$ zusätzlich surjektiv, dann ist die Zuordnung \begin{equation*} \begin{matrix} \{\text{Ideale in }S \} & → & \{ \text{Ideale $J$ in $R$ mit $\ker ψ ⊆ J$}\} \\ @@ -260,10 +259,10 @@ Formulierung verwendet Notation~\ref{not:xx}. Die Diskussion in Abschnitt~\ref{sec:10-3} wirft die Frage auf, wann ein Restklassenring der Form $K[x]/(f)$ eigentlich ein Körper ist. Etwas bescheidener: Wann ist ein Restklassenring $R/I$ nullteilerfrei? Für den Ring -$ℤ$ haben wir die Antwort in der Vorlesung ``Lineare Algebra'' kennengelernt. -Der Ring $ℤ/(m)$ ist genau dann nullteilerfrei, wenn er ein Körper ist, und dies -ist genau dann der Fall, wenn $m$ eine Primzahl ist. Also müssen wir statt -``Primzahl'' jetzt den Begriff des ``Primideals'' einführen. +$ℤ$ haben wir die Antwort in der Vorlesung „Lineare Algebra“ kennengelernt. Der +Ring $ℤ/(m)$ ist genau dann nullteilerfrei, wenn er ein Körper ist, und dies ist +genau dann der Fall, wenn $m$ eine Primzahl ist. Also müssen wir statt +„Primzahl“ jetzt den Begriff des „Primideals“ einführen. \begin{defn}[Primideal] Es sei $R$ ein kommutativer Ring mit Eins. Ein Ideal $I ⊂ R$ heißt @@ -355,7 +354,7 @@ lösbar ist. \end{definition} \begin{bemerkung} - Was hat diese Definition mit ``Teilerfremdheit'' zu tun? Schauen Sie sich den + Was hat diese Definition mit „Teilerfremdheit“ zu tun? Schauen Sie sich den Euklidischen Algorithmus aus Beispiel~\vref{bsp:5-6-7} noch einmal an. In der Situation des Beispiels~\ref{bsp:5-6-7} sind zwei Elemente $f$ und $g$ gegeben. Wenn $f$ und $g$ teilerfremd sind, ist $\ggT(f,g)=1$. Der @@ -364,12 +363,12 @@ lösbar ist. dass $(f) + (g)$ der gesamte Ring ist. \end{bemerkung} -\begin{satz}[Chinesischer Restsatz]\label{Satz_Chinesischer_Restsatz} +\begin{satz}[Chinesischer Restsatz]\label{Satz_Chinesischer_Restsatz}% \index{Chinesischer Restsatz}Es sei $R$ ein kommutativer Ring mit Eins und es seien $I_1, …, I_n ⊂ R$ paarweise teilerfremde Ideale. Dann ist der kanonische Ringhomomorphismus \begin{equation*} - α : R → \underbrace{\factor{R}{I_1}⨯⋯⨯\factor{R}{I_n}}_{\genfrac{}{}{0pt}{1}{\text{Add. und Mult.}}{\text{komponentenweise}}}, \quad a ↦ \Bigl( a+I_1, …, a+ I_n \Bigr) + α : R → \underbrace{\factor{R}{I_1}⨯⋯⨯\factor{R}{I_n}}_{\genfrac{}{}{0pt}{1}{\text{Add.~und Mult.}}{\text{komponentenweise}}}, \quad a ↦ \Bigl( a+I_1, …, a+ I_n \Bigr) \end{equation*} surjektiv und es ist $\ker α = I_1 ∩ ⋯ ∩ I_n$. \end{satz} diff --git a/12.tex b/12.tex index d44e04f..533fc59 100644 --- a/12.tex +++ b/12.tex @@ -5,10 +5,10 @@ \section{Worum geht es in diesem Teil der Vorlesung?} -Wir sind immer noch an ``Symmetrien vor Körpererweiterungen'' interessiert, aber +Wir sind immer noch an „Symmetrien vor Körpererweiterungen“ interessiert, aber ich habe ihnen bislang nicht erklärt, was ich damit meine. Das einfachste Beispiel ist vielleicht die Körpererweiterung $ℂ/ℝ$. In diesem Fall ist die -relevante ``Symmetrie'' die komplexe Konjugation, also die Spiegelung der +relevante „Symmetrie“ die komplexe Konjugation, also die Spiegelung der komplexen Ebene an der reellen Gerade. Die komplexe Konjugation ist ein Körpermorphismus $ℂ → ℂ$ (sogar ein Isomorphismus) mit der interessanten Eigenschaft, dass die reellen Zahlen genau diejenigen Punkte der komplexen Ebene @@ -18,12 +18,12 @@ und $ℝ$ vom höheren Standpunkt aus verstehen. Warum ist die Erweiterung $ℂ so wichtig? Wenn ich statt $ℝ$ einen anderen Körper betrachte (zum Beispiel $𝔽_p(X)$), welcher Körper würde dann die Rolle von $ℂ$ spielen? -Die Antwort kommt aus der Vorlesung ``Analysis'' oder ``Funktionentheorie''. -Dort beweist man mit analytischen Methoden, dass jedes Polynom $f ∈ ℝ[x]$ eine +Die Antwort kommt aus der Vorlesung „Analysis“ oder „Funktionentheorie“. Dort +beweist man mit analytischen Methoden, dass jedes Polynom $f ∈ ℝ[x]$ eine komplexe Nullstelle besitzt -- und auch jedes komplexe Polynom $f ∈ ℝ[x]$ besitzt eine komplexe Nullstelle. Das führt dazu, dass jedes Polynom in $ℂ[x]$ -als Produkt von linearen Polynome geschrieben werden kann. Man sagt: ``die -komplexen Zahlen sind algebraisch abgeschlossen''. Wir werden später sehen, was +als Produkt von linearen Polynome geschrieben werden kann. Man sagt: „Die +komplexen Zahlen sind algebraisch abgeschlossen.“. Wir werden später sehen, was diese Eigenschaft mit Symmetrie zu tun hat. \begin{frage} @@ -45,10 +45,7 @@ Oberkörper hat. Der Beweis von Satz~\ref{satz:12-1-2} ist eine große Tautologie, verwirrt Studentinnen und Studenten oft. Ich diskutiere vor dem Beweis deshalb erst noch -ein kleines Beispiel. Auf unserem -\href{https://sage.cplx.vm.uni-freiburg.de/share/}{Sage/CoCalc-Server} habe ich -Ihnen ein weiteres, ganz konkretes Beispiel bereitgestellt. - +ein kleines Beispiel. \begin{erkl} Das Polynom $x²+1 ∈ ℝ[x]$ hat keine Nullstelle in $ℝ$, aber es hat eine Nullstelle in $ℂ$, nämlich die Zahl $i$; wir wissen natürlich auch noch, dass @@ -122,7 +119,7 @@ wirklich sein soll. $f ∈ \overline{K}[x]$ ein nicht-konstantes Polynom. Weil $L$ algebraisch abgeschlossen ist, hat $f$ eine Nullstelle in $a∈ L$. Das Element $a$ ist logischerweise algebraisch über $\overline{K}$ und deshalb wegen - Korollar~\vref{kor:TdA} (``Transitivität der Algebraizität'') auch algebraisch + Korollar~\vref{kor:TdA} („Transitivität der Algebraizität“) auch algebraisch über $K$. Also ist $a∈\overline{K}$. \end{bsp} @@ -156,12 +153,12 @@ anzuwenden und so sicherzustellen, dass jedes Polynom eine Nullstelle hat. Das ist aber nicht so einfach: denn wenn ich den Körper durch Hinzunahme von Polynomen größer mache, gibt es neue Polynome, die ebenfalls Nullstellen haben müssen. In einem normalen Jahr würde mithilfe von Zorn's Lemma\footnote{Zorn's - Lemma = eine Variante des Auswahlaxioms} zeigen, dass diese naive Idee +Lemma = eine Variante des Auswahlaxioms} zeigen, dass diese naive Idee tatsächlich trägt. Weil das Semester in diesem Jahr deutlich kürzer ist, muss an dieser Stelle auf einen Beweis verzichten. Der folgende Satz ist als Satz von Steinitz\footnote{\href{https://de.wikipedia.org/wiki/Ernst_Steinitz}{Ernst - Steinitz} (* 13. Juni 1871 in Laurahütte, Oberschlesien; † 29. September - 1928 in Kiel) war ein deutscher Mathematiker.} bekannt. +Steinitz} (* 13.~Juni 1871 in Laurahütte, Oberschlesien; † 29.~September 1928 in +Kiel) war ein deutscher Mathematiker.} bekannt. \begin{satz}[Existenz des Algebraischen Abschluss]\label{Satz_von_Steinitz} Jeder Körper besitzt einen algebraischen Abschluss. \qed @@ -173,7 +170,7 @@ von Steinitz\footnote{\href{https://de.wikipedia.org/wiki/Ernst_Steinitz}{Ernst Als Nächstes müssen wir diskutieren, inwieweit ein algebraischer Abschluss eindeutig ist. Wie immer folgt die Eindeutigkeit aus einer universellen Eigenschaft. Den folgenden Begriff hatten wir oben schon informell unter dem -Schlagwort ``Symmetrien einer Körpererweiterung'' diskutiert. +Schlagwort „Symmetrien einer Körpererweiterung“ diskutiert. \begin{definition}[$K$-Morphismus] Es seien $R$ und $S$ Oberringe desselben Unterringes $K$. Ein Ringmorphismus @@ -215,7 +212,7 @@ werde ich den Satz aus Zeitgründen nicht beweisen. Als Konsequenz der universellen Eigenschaft erhalten wir die Eindeutigkeit des algebraischen Abschlusses bis auf nicht-kanonische Isomorphie. Obwohl die Isomorphie nicht kanonisch ist, spricht man in der Literatur häufig nicht ganz -korrekt von ``dem'' Quotientenkörper. +korrekt von „dem“ algebraischen Abschluss. \begin{kor}[Eindeutigkeit des alg.~Abschluss bis auf nicht-kanonische Isomorphie]\label{cor:edaa} Es sei $K$ ein Körper und es seien $\overline{K}_1$ und $\overline{K}_2$ zwei @@ -234,7 +231,7 @@ korrekt von ``dem'' Quotientenkörper. Ich wiederhole noch einmal: Die nicht-Eindeutigkeit der Abbildung $\varphi$ aus Satz~\ref{Satz_K_Morphismus_Fortsetzung} und nicht-Kanonizität der Abbildung aus Korollar~\ref{cor:edaa} sind der Grund dafür, warum die Diskussion von -``Symmetrie'' überhaupt sinnvoll ist. Das ist ganz anders als bei dem +„Symmetrie“ überhaupt sinnvoll ist. Das ist ganz anders als bei dem Quotientenkörper! diff --git a/13.tex b/13.tex index f2bf86d..e384103 100644 --- a/13.tex +++ b/13.tex @@ -3,16 +3,16 @@ \chapter{Zerfällungskörper} -Ich habe im vorhergehenden Kapitel immer wieder von ``Symmetrie'' gesprochen und +Ich habe im vorhergehenden Kapitel immer wieder von „Symmetrie“ gesprochen und dabei als Beispiel immer nur die Konjugationsabbildung der komplexen Zahlen diskutiert. Das ist ein bisschen dünn. Wir brauchen mehr Beispiele! Tatsächlich liefert fast jedes Polynom ein interessantes Beispiel, den Zerfällungskörper. Was das ist, erkläre ich jetzt. -\begin{defn}[Zerfällungskörper]\label{def:zerf} +\begin{defn}[Zerfällungskörper]\label{def:zerf}% Es sei $K$ ein Körper und es sei $f ∈ K[x]$ ein nicht-konstantes Polynom. Ein Oberkörper $L/K$ heißt \emph{Zerfällungskörper von - $f$}\index{Zerfällungskörper}, falls Folgendes gilt. + $f$}\index{Zerfällungskörper}, falls Folgendes gilt. \begin{itemize} \item Das Polynom $f ∈ L[x]$ zerfällt in Linearfaktoren. Mit anderen Worten: es gibt Elemente $a, a_1, …, a_n ∈ L$, sodass die Gleichheit @@ -24,7 +24,7 @@ Zerfällungskörper. Was das ist, erkläre ich jetzt. \begin{bemerkung} Die Elemente $a_1, …, a_n$ aus Definition~\ref{def:zerf} sind genau die - Nullstellen des Polynomes $f ∈ L[x]$. Insbesondere sind die Elemente + Nullstellen des Polynoms $f ∈ L[x]$. Insbesondere sind die Elemente $a_1, …, a_n$ eindeutig bis auf Vertauschung. \end{bemerkung} @@ -53,16 +53,16 @@ schon beim algebraischen Abschluss wird deshalb häufig von ``dem'' Zerfällungskörper gesprochen. \begin{bemerkung}[Kochrezept: Zerfällungskörper] - Es sei $K$ ein Körper und es sei $f ∈ K[x]$ ein nicht-konstantes Polynom. - Wenn ein algebraischer abgeschlossener Oberkörper $L/K$ gegeben ist, dann - zeigt der Beweis von Satz~\ref{satz:13-0-3} wie man an einen Zerfällungskörper - kommt. Man muss für das Polynom $f ∈ L[x]$ ``lediglich'' die Nullstellen - $a_1, …, a_n$ bestimmen und kann dann den Körper $K(a_1, …, a_n)$ nehmen. + Es sei $K$ ein Körper und es sei $f ∈ K[x]$ ein nicht-konstantes Polynom. Wenn + ein algebraischer abgeschlossener Oberkörper $L/K$ gegeben ist, dann zeigt der + Beweis von Satz~\ref{satz:13-0-3} wie man an einen Zerfällungskörper kommt. + Man muss für das Polynom $f ∈ L[x]$ „lediglich“ die Nullstellen $a_1, …, a_n$ + bestimmen und kann dann den Körper $K(a_1, …, a_n)$ nehmen. \end{bemerkung} Ein wichtiges Problem der Algebra(klausur/prüfung) ist es, zu einem gegebenen Körper $K$ und zu einem gegebenen Polynom $f ∈ K[x]$ den Zerfällungskörper zu -bestimmen. Dabei ist mit ``bestimmen'' meistens gemeint, dass man den +bestimmen. Dabei ist mit „bestimmen“ meistens gemeint, dass man den Erweiterungsgrad des Zerfällungskörpers bestimmen und ein möglichst kleinen Satz von möglichst einfachen Erzeugern angeben soll. Meistens ist in diesen Beispielen $K = ℚ$, sodass man einen Zerfällungskörper als Teilmenge der @@ -87,11 +87,10 @@ komplexen Zahlen konstruieren wird. \[ [L : ℚ] ≤ 3! = 6, \] - ist, aber wie groß ist der Grad wirklich? Wir überlegen, dass - $[ℚ \bigl(\sqrt[3]{2} \bigr) : ℚ ] = 3$. Also gilt $3| [L:Q]$ und man - muss lediglich prüfen, ob $L = ℚ(\sqrt[3]{2})$ ist. Das ist aber nicht der - Fall, denn $ℚ(\sqrt[3]{2}) ⊂ ℝ$ aber $ξ \not∈ ℝ$. Also ist - $[L:ℚ] =6$. + ist, aber wie groß ist der Grad wirklich? Wir überlegen, dass $[ℚ + \bigl(\sqrt[3]{2} \bigr) : ℚ ] = 3$. Also gilt $3| [L:Q]$ und man muss + lediglich prüfen, ob $L = ℚ(\sqrt[3]{2})$ ist. Das ist aber nicht der Fall, + denn $ℚ(\sqrt[3]{2}) ⊂ ℝ$ aber $ξ \not∈ ℝ$. Also ist $[L:ℚ] =6$. \end{bsp} @@ -99,7 +98,7 @@ komplexen Zahlen konstruieren wird. \label{sec:13-1} \sideremark{Vorlesung 14}Ich komme zu meinem Lieblingsthema zurück. Jetzt kann -ich endlich erklären, was es mit meinem ständigen Reden von ``Symmetrien'' auf +ich endlich erklären, was es mit meinem ständigen Reden von „Symmetrien“ auf sich hat. \begin{situation}\label{sit:gal} @@ -141,13 +140,13 @@ das wohl am besten in Termen endlicher Gruppen beantwortet werden sollte. Wenn ich jetzt einen $K$-Morphismus $\varphi: L → L$ habe, dann ist \begin{align*} \varphi(ℓ) & = \sum \varphi(β_{i_1,…,i_n})·\varphi(a_1)^{i_1}⋯ \varphi(a_n)^{i_n} \\ - & = \sum β_{i_1,…,i_n}·\varphi(a_1)^{i_1}⋯ \varphi(a_n)^{i_n}. && \text{$\varphi$ ist $K$-Morphismus und $β_• ∈ K$} + & = \sum β_{i_1,…,i_n}·\varphi(a_1)^{i_1}⋯ \varphi(a_n)^{i_n}. && \text{$\varphi$ ist $K$-Morphismus und $β_• ∈ K$.} \end{align*} Wir erkennen: Der $K$-Morphismus $\varphi: L → L$ ist eindeutig dadurch - festgelegt, wohin er die endlich vielen Elemente $a_1$, …, $a_n$ abbildet! - Die Abbildung \eqref{eq:jtzrtt} ist also injektiv, und wir können die - ``Symmetriegruppe'' von $L/K$, also die Gruppe der $K$-Isomorphismen von $L$ - als Untergruppe einer endlichen Permutationsgruppe auffassen. + festgelegt, wohin er die endlich vielen Elemente $a_1$, …, $a_n$ abbildet! Die + Abbildung \eqref{eq:jtzrtt} ist also injektiv, und wir können die + „Symmetriegruppe“ von $L/K$, also die Gruppe der $K$-Isomorphismen von $L$ als + Untergruppe einer endlichen Permutationsgruppe auffassen. \end{beobachtung} @@ -163,7 +162,7 @@ ein wenig Sprache. vielen) Variablen $(x_λ)_{λ∈ Λ}$. \end{notation} -Wenn alles 100\%ig korrekt sein sollte, müsste ich an dieser könnte den +Wenn alles 100\%ig korrekt sein sollte, müsste ich an dieser Stelle den Polynomring ausführlich mithilfe einer universellen Eigenschaft definieren. Ich finde das aber arg formell und hoffe, Sie verzeihen mir, wenn ich das jetzt einfach mal nicht mache. Der einzig wichtige Punkt ist, dass Polynome immer @@ -197,7 +196,7 @@ immer nur endlich viele Variablen auf. \end{beobachtung} -\subsection{Ringadjunktion vs Körperadjunktion} +\subsection{Ringadjunktion vs.~Körperadjunktion} Gegeben eine Körpererweiterung $L/K$ und eine Teilmenge $(a_λ)_{λ∈Λ}$ von $L$, dann kann ich den Unterring $K\bigl[(a_λ)_{λ∈Λ}\bigr]$ und den Unterkörper @@ -207,9 +206,9 @@ $K\bigl( (a_λ)_{λ∈Λ} \bigr)$ vergleichen. Offenbar gilt immer ⊆ L. \] Die folgenden Sätze klären, wann Gleichheit herrscht. Die Sätze klären auch -noch einmal, warum SAGE eckige Klammern verwendet und den Körper ``$ℚ$ -adjungiert $\sqrt{5}$'' mit \texttt{QQ[sqrt(5)]} bezeichnet. Schauen Sie sich -vielleicht auch noch einmal Fußnote~\vref{foot:sage} an. +noch einmal, warum SAGE eckige Klammern verwendet und den Körper „$ℚ$ adjungiert +$\sqrt{5}$“ mit \texttt{QQ[sqrt(5)]} bezeichnet. Schauen Sie sich vielleicht +auch noch einmal Fußnote~\vref{foot:sage} an. \begin{satz}[Ringadjunktion vs Körperadjunktion] Es sei $L/K$ eine Körpererweiterung und es sei $(a_λ)_{λ∈Λ}$ eine Teilmenge diff --git a/14.tex b/14.tex index ea4381a..e92534c 100644 --- a/14.tex +++ b/14.tex @@ -132,23 +132,23 @@ bestimmen. Was war noch einmal die Ordnung? \end{beobachtung} -\section{Der Frobenius Morphismus} +\section{Der Frobenius-Morphismus} Über Körpern und Ringen der Charakteristik $p > 0$ gibt es einen ganz unglaublichen Körpermorphismus, den wir noch nicht kennen: den Frobenius-Morphismus\footnote{\href{https://de.wikipedia.org/wiki/Ferdinand_Georg_Frobenius}{Ferdinand - Georg Frobenius}, genannt Georg, (* 26. Oktober 1849 in Berlin; † 3. - August 1917 in Charlottenburg, heute ein Ortsteil von Berlin) war ein - deutscher Mathematiker. Er war seit 1892 Professor an der Universität Berlin - und setzte dort hohe Maßstäbe für Prüfungen durch.}. Der Morphismus ist -eigentlich ganz einfach, es handelt sich um die Abbildung $r ↦ r^p$. Das -unglaubliche ist, dass diese Abbildung \textbf{linear} ist!! +Georg Frobenius}, genannt Georg, (* 26.~Oktober 1849 in Berlin; † 3.~August 1917 +in Charlottenburg, heute ein Ortsteil von Berlin) war ein deutscher +Mathematiker. Er war seit 1892 Professor an der Universität Berlin und setzte +dort hohe Maßstäbe für Prüfungen durch.}. Der Morphismus ist eigentlich ganz +einfach, es handelt sich um die Abbildung $r ↦ r^p$. Das unglaubliche ist, dass +diese Abbildung \textbf{linear} ist! \begin{defn}[Charakeristik eines Ringes] Es sei $R$ ein kommutativer Ring mit Eins. Die \emph{Charakteristik}\index{Charakteristik!eines Ringes} von $R$ ist die kleinste natürliche Zahl $n ∈ ℕ^+$, sodass die $n$-fache Summe des - Einselementes gleich dem Nullelement wird, also + Einselements gleich dem Nullelement wird, also \[ \underbrace{1 + 1 + ⋯ + 1}_{n ⨯} =0. \] @@ -174,8 +174,8 @@ unglaubliche ist, dass diese Abbildung \textbf{linear} ist!! \begin{notation} In der Situation von Satz~\ref{DefSatz_Frobenius-Endomorphismus} ist die - Bildmenge $F(R) ⊂ R$ natürlich ein Unterring. Dieser wird als ``Menge der - $p$-Potenzen'' bezeichnet und oft mit dem Symbol $R^p ⊆ R$ notiert. + Bildmenge $F(R) ⊂ R$ natürlich ein Unterring. Dieser wird als „Menge der + $p$-Potenzen“ bezeichnet und oft mit dem Symbol $R^p ⊆ R$ notiert. \end{notation} \begin{beobachtung} @@ -190,7 +190,7 @@ unglaubliche ist, dass diese Abbildung \textbf{linear} ist!! \section{Separable und inseparable Polynome} Ich hatte oben gefragt, ob ein irreduzibles Polynom mehrfache Nullstellen haben -kann. Die ehrliche Antwort lautet: ``vielleicht'' und begründet die folgende +kann. Die ehrliche Antwort lautet: „vielleicht“ und begründet die folgende Definition. \begin{defn}[Separable und inseparable Polynome] @@ -288,7 +288,7 @@ werden. \begin{bsp} Sei $K = 𝔽_p(t) = Q\bigl( 𝔽_p[t] \bigr)$. Nach dem - Satz~\vref{Satz_Eisenstein_Kriterium} (``Eisenstein-Kriterium'') ist + Satz~\vref{Satz_Eisenstein_Kriterium} („Eisenstein-Kriterium“) ist \begin{equation*} f = x^p-t ∈ K[x] \end{equation*} @@ -347,7 +347,7 @@ Erweiterungen kennen. Die gesamte Diskussion baut auf folgendem Lemma auf. $σ : K(a) → L$. \end{lemma} \begin{proof} - Ich erinnere an die Beobachtungen~\ref{beob:p1} und \vref{beob:p2}: jeder + Ich erinnere an die Beobachtungen~\ref{beob:p1} und \vref{beob:p2}: Jeder potenzielle $K$-Morphismus $σ$ bildet $a$ auf eine der $m$ Nullstellen von $f$ an, und ist durch dieses Bild eindeutig festgelegt. Jetzt müssen wir lediglich noch zeigen, dass jede dieser $m$ verschiedenen Möglichkeiten @@ -370,8 +370,8 @@ Erweiterungen kennen. Die gesamte Diskussion baut auf folgendem Lemma auf. Mit diesen Vorbereitungen können wir separable Abbildungen in präziser Art durch die Anzahl von $K$-Morphismen charakterisieren. Als Konsequenz erhalten wir -eine Reihe von Sätzen, die wir für den Begriff der ``algebraischen -Körpererweiterung'' in ganz ähnlicher Form schon kennen. +eine Reihe von Sätzen, die wir für den Begriff der „algebraischen +Körpererweiterung“ in ganz ähnlicher Form schon kennen. \begin{satz}\label{Satz_11_10} Es sei $L/K$ eine endliche (also insbesondere: algebraische) Körpererweiterung @@ -424,8 +424,8 @@ Körpererweiterung'' in ganz ähnlicher Form schon kennen. \subsection{Der separable Abschluss} -Erinnern Sie sich an den ``algebraischen Abschluss einer Körpers in einem -Oberkörper'', den wir in Satz~\vref{satzdef:aaieO} eingeführt haben? Auch +Erinnern Sie sich an den „algebraischen Abschluss eines Körpers in einem +Oberkörper“, den wir in Satz~\vref{satzdef:aaieO} eingeführt haben? 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Preprint \href{https://arxiv.org/abs/1407.3431}{arXiv:1407.3431}.}, - PAGES = {2350--2370}, - ISSN = {0010-437X}, - MRCLASS = {32Q05 (32Q10 32Q15 32Q20 32U05 32U15)}, - MRNUMBER = {3577897}, -MRREVIEWER = {Cezar Joi\c{t}a}, - DOI = {10.1112/S0010437X16007442}, - URL = {https://doi.org/10.1112/S0010437X16007442}, -} - -@article {CP15, - AUTHOR = {Campana, Frédéric and Păun, Mihai}, - TITLE = {Orbifold generic semi-positivity: an application to families of canonically polarized manifolds}, - JOURNAL = {Ann. Inst. Fourier (Grenoble)}, - FJOURNAL = {Université de Grenoble. Annales de l'Institut Fourier}, - VOLUME = 65, - YEAR = 2015, - NUMBER = 2, - NOTE = {\href{https://doi.org/10.5802/aif.2945}{DOI:10.5802/aif.2945}. 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Korányi}, -} - -@article{MR0186672, - Author = {Lipman, Joseph}, - Fjournal = {American Journal of Mathematics}, - Issn = {0002-9327}, - Journal = {Amer. J. Math.}, - Mrclass = {14.52}, - Mrnumber = {0186672 (32 \#4130)}, - Mrreviewer = {M. Nagata}, - Pages = {874--898}, - Title = {Free derivation modules on algebraic varieties}, - Volume = 87, - Year = 1965 -} - -@article{MR0190143, - Author = {{\v{S}}afarevi{\v{c}}, I. R. and Averbuh, B. G. and - Va{\u\i}nberg, Ju. R. and {\v{Z}}i{\v{z}}{\v{c}}enko, - A. B. and Manin, Ju. I. and Mo{\u\i}{\v{s}}ezon, B. G. and - Tjurina, G. N. and Tjurin, A. N.}, - Fjournal = {Akademiya Nauk SSSR. Trudy Matematicheskogo Instituta imeni - V. A. Steklova}, - Issn = {0371-9685}, - Journal = {Trudy Mat. Inst. Steklov.}, - Mrclass = {14.20}, - Mrnumber = {0190143 (32 \#7557)}, - Mrreviewer = {E. C. Dade}, - Pages = {1--215}, - Title = {Algebraic surfaces}, - Volume = 75, - Year = 1965 -} - -@article{MR0199191, - Author = {Artin, Michael}, - Fjournal = {American Journal of Mathematics}, - Issn = {0002-9327}, - Journal = {Amer. J. Math.}, - Mrclass = {14.18 (14.20)}, - Mrnumber = {0199191 (33 \#7340)}, - Mrreviewer = {P. Du Val}, - Pages = {129--136}, - Title = {On isolated rational singularities of surfaces}, - Volume = 88, - Year = 1966 -} - -@book{MR0202713, - Author = {Hirzebruch, Friedrich}, - Mrclass = {14.00 (32.00)}, - Mrnumber = {0202713 (34 \#2573)}, - Mrreviewer = {M. F. Atiyah}, - Pages = {x+232}, - Publisher = {Springer-Verlag New York, Inc., New York}, - Series = {Third enlarged edition. New appendix and translation from the - second German edition by R. L. E. Schwarzenberger, with an - additional section by A. Borel. Die Grundlehren der - Mathematischen Wissenschaften, Band 131}, - Title = {Topological methods in algebraic geometry}, - Year = 1966 -} - -@article {MR0204430, - AUTHOR = {Samuel, Pierre}, - TITLE = {Compléments à un article de {H}ans {G}rauert sur la conjecture - de {M}ordell}, - JOURNAL = {Inst. Hautes Études Sci. Publ. Math.}, - FJOURNAL = {Institut des Hautes Études Scientifiques. Publications - Mathématiques}, - NOTE = - {\href{http://www.numdam.org/item?id=PMIHES_1966__29__55_0}{numdam.PMIHES-1966-29-55-0}}, - NUMBER = 29, - YEAR = 1966, - PAGES = {55--62}, - ISSN = {0073-8301}, - MRCLASS = {14.49 (14.40)}, - MRNUMBER = 0204430, - MRREVIEWER = {J. V. Armitage}, - URL = {http://www.numdam.org/item?id=PMIHES_1966__29__55_0}, -} - -@article{MR0210944, - Author = {Prill, David}, - Fjournal = {Duke Mathematical Journal}, - Issn = {0012-7094}, - Journal = {Duke Math. J.}, - Mrclass = {32.65 (10.23)}, - Mrnumber = {0210944 (35 \#1829)}, - Mrreviewer = {E. Brieskorn}, - Pages = {375--386}, - Title = {Local classification of quotients of complex manifolds by - discontinuous groups}, - Volume = 34, - Year = 1967 -} - -@article {MR0212214, - AUTHOR = {Serre, Jean-Pierre}, - TITLE = {Prolongement de faisceaux analytiques cohérents}, - JOURNAL = {Ann. Inst. Fourier (Grenoble)}, - FJOURNAL = {Université de Grenoble. Annales de l'Institut Fourier}, - VOLUME = 16, - YEAR = 1966, - NUMBER = {fasc. 1}, - PAGES = {363--374}, - ISSN = {0373-0956}, - MRCLASS = {32.50 (32.27)}, - MRNUMBER = 0212214, - MRREVIEWER = {B. Shiffman}, - URL = {http://www.numdam.org/item?id=AIF_1966__16_1_363_0}, -} - -@article {MR0222087, - AUTHOR = {Grauert, Hans}, - TITLE = {Mordells {V}ermutung über rationale {P}unkte auf algebraischen - {K}urven und {F}unktionenkörper}, - JOURNAL = {Inst. Hautes Études Sci. Publ. Math.}, - FJOURNAL = {Institut des Hautes Études Scientifiques. Publications - Mathématiques}, - NOTE = - {\href{http://www.numdam.org/item?id=PMIHES_1965__25__131_0}{numdam.PMIHES-1965-25-131-0}}, - NUMBER = 25, - YEAR = 1965, - PAGES = {131--149}, - ISSN = {0073-8301}, - MRCLASS = {14.40 (10.00)}, - MRNUMBER = 0222087, - MRREVIEWER = {M. Miwa}, - URL = {http://www.numdam.org/item?id=PMIHES_1965__25__131_0}, -} - -@book {MR0222088, - AUTHOR = {Samuel, Pierre}, - TITLE = {Lectures on old and new results on algebraic curves}, - SERIES = {Notes by S. Anantharaman. Tata Institute of Fundamental - Research Lectures on Mathematics, No. 36}, - PUBLISHER = {Tata Institute of Fundamental Research, Bombay}, - NOTE = {Available on the internet at - \href{http://www.math.tifr.res.in/~publ/ln/index.html}{www.math.tifr.res.in/$\sim$publ/ln/index.html}}, - YEAR = 1966, - PAGES = {ii+127+iii}, - MRCLASS = {14.40 (10.00)}, - MRNUMBER = 0222088, - MRREVIEWER = {M. Miwa}, -} - -@article {MR0223368, - AUTHOR = {Shimura, Goro}, - TITLE = {Algebraic varieties without deformation and the {C}how - variety}, - JOURNAL = {J. Math. Soc. Japan}, - FJOURNAL = {Journal of the Mathematical Society of Japan}, - VOLUME = 20, - YEAR = 1968, - PAGES = {336--341}, - ISSN = {0025-5645}, - MRCLASS = {14.20}, - MRNUMBER = 0223368, - MRREVIEWER = {S. Lubkin}, -} - -@book{MR0242802, - Author = {Atiyah, Michael F. and Macdonald, Ian G.}, - Mrclass = {13.00}, - Mrnumber = {0242802 (39 \#4129)}, - Mrreviewer = {J. A. Johnson}, - Pages = {ix+128}, - Publisher = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don - Mills, Ont.}, - Title = {Introduction to commutative algebra}, - Year = 1969 -} - -@article{MR0245837, - Author = {Siu, Yum-tong}, - Fjournal = {Annals of Mathematics. Second Series}, - Issn = {0003-486X}, - Journal = {Ann. of Math. (2)}, - Mrclass = {32.50}, - Mrnumber = {0245837 (39 \#7143)}, - Mrreviewer = {G. Trautmann}, - Pages = {108--143}, - Title = {Extending coherent analytic sheaves}, - Volume = 90, - Year = 1969 -} - -@book {MR0252690, - AUTHOR = {Piatetski-Shapiro, Ilya I.}, - TITLE = {Automorphic functions and the geometry of classical domains}, - SERIES = {Translated from the Russian. Mathematics and Its Applications, - Vol. 8 }, - PUBLISHER = {Gordon and Breach Science Publishers, New York-London-Paris}, - YEAR = 1969, - PAGES = {viii+264}, - MRCLASS = {32.65}, - MRNUMBER = 0252690, -} - -@article{MR0257070, - Author = {Storch, Uwe}, - Fjournal = {Mathematische Annalen}, - Issn = {0025-5831}, - Journal = {Math. Ann.}, - Mrclass = {13.95 (32.00)}, - Mrnumber = {0257070 (41 \#1724)}, - Mrreviewer = {E. Brieskorn}, - Pages = {93--104}, - Title = {{ü}ber die {D}ivisorenklassengruppen normaler - komplexanalytischer {A}lgebren}, - Volume = 183, - Year = 1969 -} - -@book {MR0260758, - AUTHOR = {Raynaud, Michel}, - TITLE = {Faisceaux amples sur les schémas en groupes et les espaces homogènes}, - SERIES = {Lecture Notes in Mathematics, Vol. 119}, - PUBLISHER = {Springer-Verlag, Berlin-New York}, - YEAR = {1970}, - PAGES = {ii+218}, - MRCLASS = {14.55}, - MRNUMBER = {0260758}, - NOTE = {\href{https://doi.org/10.1007/BFb0059504}{DOI:10.1007/BFb0059504}}, -MRREVIEWER = {D. Gieseker}, -} - -@incollection {MR0261635, - AUTHOR = {Baum, Paul F. and Bott, Raoul}, - TITLE = {On the zeros of meromorphic vector-fields}, - BOOKTITLE = {Essays on {T}opology and {R}elated {T}opics ({M}émoires dédiés à {G}eorges de {R}ham)}, - PAGES = {29--47}, - PUBLISHER = {Springer, New York}, - YEAR = {1970}, - MRCLASS = {57.60 (32.00)}, - MRNUMBER = {0261635}, -MRREVIEWER = {H. Suzuki}, - NOTE = {\href{https://doi.org/10.1007/978-3-642-49197-9_4}{DOI:10.1007/978-3-642-49197-9\_4}}, -} - -@article{MR0262386, - Author = {Grothendieck, Alexander}, - Fjournal = {Manuscripta Mathematica}, - Issn = {0025-2611}, - Journal = {Manuscripta Math.}, - Mrclass = {20.80 (14.00)}, - Mrnumber = {0262386 (41 \#6994)}, - Mrreviewer = {F. Oort}, - Note = - {\href{https://doi.org/10.1007/BF01719593}{DOI:10.1007/BF01719593}}, - Pages = {375--396}, - Title = {Représentations linéaires et compactification profinie des - groupes discrets}, - Volume = 2, - Year = 1970 -} - -@book{MR0278248, - Address = {Berlin}, - Author = {Lascoux, Alain and Berger, Marcel}, - Mrclass = {53.80 (14.00)}, - Mrnumber = {0278248 (43 \#3979)}, - Mrreviewer = {T. Ochiai}, - Pages = {vii+83}, - Publisher = {Springer-Verlag}, - Series = {Lecture Notes in Mathematics, Vol. 154}, - Title = {Variétés {K}ähleriennes compactes}, - Year = 1970 -} - -@article {MR0279338, - AUTHOR = {Ramis, Jean-Pierre and Ruget, Gabriel}, - TITLE = {Complexe dualisant et théorèmes de dualité en géométrie - analytique complexe}, - JOURNAL = {Inst. Hautes Études Sci. Publ. Math.}, - FJOURNAL = {Institut des Hautes Études Scientifiques. Publications - Mathématiques}, - NUMBER = 38, - Note = - {\href{http://www.numdam.org/item?id=PMIHES_1970__38__77_0}{numdam.PMIHES-1970-38-77-0}}, - YEAR = 1970, - PAGES = {77--91}, - ISSN = {0073-8301}, - MRCLASS = {32.50}, - MRNUMBER = 0279338, - MRREVIEWER = {Y.-T. Siu}, - URL = {http://www.numdam.org/item?id=PMIHES_1970__38__77_0}, -} - -@book{MR0287033, - Address = {Berlin}, - Author = {Siu, Yum-Tong and Trautmann, Günther}, - Mrclass = {32.50}, - Mrnumber = {0287033 (44 \#4240)}, - Mrreviewer = {W. Thimm}, - NOTE = - {\href{https://doi.org/10.1007/BFb0060577}{DOI:10.1007/BFb0060577}}, - Pages = {v+172}, - Publisher = {Springer-Verlag}, - Series = {Lecture Notes in Mathematics, Vol. 172}, - Title = {Gap-sheaves and extension of coherent analytic subsheaves}, - Year = 1971 -} - -@article{MR0306172, - Author = {Scheja, Günter and Storch, Uwe}, - Fjournal = {Mathematische Annalen}, - Issn = {0025-5831}, - Journal = {Math. Ann.}, - Mrclass = {13B10}, - Mrnumber = {0306172 (46 \#5299)}, - Mrreviewer = {Joseph Lipman}, - Pages = {137--170}, - Title = {Differentielle {E}igenschaften der {L}okalisierungen - analytischer {A}lgebren}, - Volume = 197, - Year = 1972 -} - -@article {MR0308439, - AUTHOR = {Ramis, Jean-Pierre and Ruget, Gabriel and Verdier, Jean-Louis}, - TITLE = {Dualité relative en géométrie analytique complexe}, - JOURNAL = {Invent. Math.}, - FJOURNAL = {Inventiones Mathematicae}, - VOLUME = 13, - YEAR = 1971, - PAGES = {261--283}, - ISSN = {0020-9910}, - MRCLASS = {32C35 (14B10)}, - MRNUMBER = 0308439, - MRREVIEWER = {W. Thimm}, - NOTE = {\href{https://doi.org/10.1007/BF01406078}{DOI:10.1007/BF01406078}}, - DOI = {10.1007/BF01406078}, - URL = {https://doi.org/10.1007/BF01406078}, -} - -@article{MR0322209, - Author = {Horikawa, Eiji}, - Journal = {J. Math. Soc. Japan}, - Mrclass = {32G99 (32C10 32H99)}, - Mrnumber = {0322209 (48 \#571)}, - Mrreviewer = {H. Kerner}, - Pages = {372--396}, - Title = {On deformations of holomorphic maps. {I}}, - Volume = 25, - Year = 1973 -} - -@book{MR0335656, - Address = {New York}, - Author = {Wehrfritz, Bertram A. F.}, - Mrclass = {20HXX}, - Mrnumber = {0335656 (49 \#436)}, - Mrreviewer = {I. Stewart}, - Note = {Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 76. \href{https://doi.org/10.1007/978-3-642-87081-1}{DOI:10.1007/978-3-642-87081-1}}, - Pages = {xiv+229}, - Publisher = {Springer-Verlag}, - Title = {Infinite linear groups. {A}n account of the group-theoretic properties of infinite groups of matrices}, - Year = 1973 -} - -@article {MR0337963, - AUTHOR = {Sumihiro, Hideyasu}, - TITLE = {Equivariant completion}, - JOURNAL = {J. Math. Kyoto Univ.}, - FJOURNAL = {Journal of Mathematics of Kyoto University}, - VOLUME = 14, - YEAR = 1974, - PAGES = {1--28}, - ISSN = {0023-608X}, - MRCLASS = {14E25 (20G99)}, - MRNUMBER = 0337963, - MRREVIEWER = {V. L. Popov}, - NOTE = {\href{https://doi.org/10.1215/kjm/1250523277}{DOI:10.1215/kjm/1250523277}}, - DOI = {10.1215/kjm/1250523277}, - URL = {https://doi.org/10.1215/kjm/1250523277}, -} - -@article{MR0344519, - Author = {Schlessinger, Michael}, - Fjournal = {Rice University Studies}, - Issn = {0035-4996}, - Journal = {Rice Univ. Studies}, - Mrclass = {32C40 (14B10)}, - Mrnumber = {0344519 (49 \#9258)}, - Mrreviewer = {Bernard Teissier}, - Note = {Complex analysis, 1972 (Proc. Conf., Rice Univ., Houston, - Tex., 1972), Vol. I: Geometry of singularities}, - Number = 1, - Pages = {147--162}, - Title = {On rigid singularities}, - Volume = 59, - Year = 1973 -} - -@book {MR0354798, - AUTHOR = {MacLane, Saunders}, - TITLE = {Categories for the working mathematician}, - NOTE = {Graduate Texts in Mathematics, Vol.~5. \href{https://doi.org/10.1007/978-1-4757-4721-8}{DOI:10.1007/978-1-4757-4721-8}}, - PUBLISHER = {Springer-Verlag, New York-Berlin}, - YEAR = {1971}, - PAGES = {ix+262}, - MRCLASS = {18-02}, - MRNUMBER = {0354798}, -MRREVIEWER = {H.-B. Brinkmann}, -} - -@article{MR0360585, - Author = {Hochster, Melvin}, - Fjournal = {Proceedings of the American Mathematical Society}, - Issn = {0002-9939}, - Journal = {Proc. Amer. Math. Soc.}, - Mrclass = {14E15 (13F99 14M10)}, - Mrnumber = {0360585 (50 \#13033)}, - Mrreviewer = {Tadayuki Matsuoka}, - Pages = {261--262}, - Title = {The {Z}ariski-{L}ipman conjecture for homogeneous complete - intersections}, - Volume = 49, - Year = 1975 -} - -@article {MR0360616, - AUTHOR = {Kleiman, Steven L.}, - TITLE = {The transversality of a general translate}, - JOURNAL = {Compositio Math.}, - FJOURNAL = {Compositio Mathematica}, - VOLUME = 28, - YEAR = 1974, - PAGES = {287--297}, - ISSN = {0010-437X}, - MRCLASS = {14M15 (14N10)}, - MRNUMBER = 0360616, - MRREVIEWER = {Joel Roberts}, - NOTE = - {\href{http://http://www.numdam.org/item?id=CM_1974__28_3_287_0}{numdam.CM-1974-28-3-287-0}}, -} - -@article {MR0370665, - AUTHOR = {Kashiwara, Masaki}, - TITLE = {On the maximally overdetermined system of linear differential - equations. {I}}, - JOURNAL = {Publ. Res. Inst. Math. Sci.}, - FJOURNAL = {Kyoto University. Research Institute for Mathematical - Sciences. Publications}, - VOLUME = 10, - YEAR = {1974/75}, - PAGES = {563--579}, - ISSN = {0034-5318}, - NOTE = - {\href{https://doi.org/10.2977/prims/1195192011}{DOI:10.2977/prims/1195192011}}, - MRCLASS = {58G15 (32C35 35N05)}, - MRNUMBER = 0370665, - MRREVIEWER = {P. Schapira}, - DOI = {10.2977/prims/1195192011}, - URL = {https://doi.org/10.2977/prims/1195192011}, -} - -@article{MR0376678, - Author = {{D}u~{B}ois, Philippe and Jarraud, Pierre}, - Journal = {C. R. Acad. Sci. Paris Sér. A}, - Mrclass = {14F05}, - Mrnumber = {0376678 (51 \#12853)}, - Mrreviewer = {J. S. Joel}, - Pages = {745--747}, - Title = {Une propriété de commutation au changement de base des images - directes supérieures du faisceau structural}, - Volume = 279, - Year = 1974 -} - -@book {MR0385004, - AUTHOR = {Mostow, G. D.}, - TITLE = {Strong rigidity of locally symmetric spaces}, - SERIES = {Annals of Mathematics Studies, No. 78}, - PUBLISHER = {Princeton University Press, Princeton, N.J.; University of - Tokyo Press, Tokyo}, - YEAR = {1973}, - PAGES = {v+195}, - MRCLASS = {22E40 (53C35)}, - MRNUMBER = {0385004}, -MRREVIEWER = {M. S. Raghunathan}, -} - -@book {MR0396773, - AUTHOR = {Humphreys, James E.}, - TITLE = {Linear algebraic groups}, - NOTE = {Graduate Texts in Mathematics, No. 21. \href{https://doi.org/10.1007/978-1-4684-9443-3}{DOI:10.1007/978-1-4684-9443-3}}, - PUBLISHER = {Springer-Verlag, New York-Heidelberg}, - YEAR = {1975}, - PAGES = {xiv+247}, - MRCLASS = {20GXX (14LXX)}, - MRNUMBER = {0396773}, -MRREVIEWER = {T. Ono}, -} - -@article {MR0397729, - AUTHOR = {Deligne, Pierre and Sullivan, Dennis}, - TITLE = {Fibrés vectoriels complexes à groupe structural discret}, - JOURNAL = {C. R. Acad. Sci. Paris Sér. A-B}, - VOLUME = 281, - YEAR = 1975, - NUMBER = 24, - PAGES = {Ai, A1081--A1083}, - MRCLASS = {55F10 (32L05)}, - MRNUMBER = 0397729, - MRREVIEWER = {P. E. Newstead}, -} - -@article{MR0404257, - Author = {Fulton, William}, - Fjournal = {Institut des Hautes Études Scientifiques. Publications - Mathématiques}, - Issn = {0073-8301}, - Journal = {Inst. Hautes Études Sci. Publ. Math.}, - Mrclass = {14C05 (14C15)}, - Mrnumber = {0404257 (53 \#8060)}, - Mrreviewer = {J.-P. Jouanolou}, - Number = 45, - Pages = {147--167}, - Title = {Rational equivalence on singular varieties}, - Year = 1975 -} - -@book{MR0447557, - Address = {Berlin}, - Author = {Forster, Otto}, - Mrclass = {30A46 (32-01)}, - Mrnumber = {0447557 (56 \#5867)}, - Mrreviewer = {H. H. Martens}, - Note = {Heidelberger Taschenbücher, Band 184}, - Pages = {x+223}, - Publisher = {Springer-Verlag}, - Title = {Riemannsche {F}lächen}, - Year = 1977 -} - -@article{MR0451180, - Author = {Yau, Shing-Tung}, - Fjournal = {Proceedings of the National Academy of Sciences of the United - States of America}, - Issn = {0027-8424}, - Journal = {Proc. Nat. Acad. Sci. U.S.A.}, - Mrclass = {53C55 (14M20 32C10)}, - Mrnumber = {0451180 (56 \#9467)}, - Mrreviewer = {Bang-yen Chen}, - Number = 5, - Pages = {1798--1799}, - Title = {Calabi's conjecture and some new results in algebraic - geometry}, - Volume = 74, - Year = 1977 -} - -@article {MR0460317, - AUTHOR = {Flenner, Hubert}, - TITLE = {Die {S}ätze von {B}ertini für lokale {R}inge}, - JOURNAL = {Math. Ann.}, - FJOURNAL = {Mathematische Annalen}, - NOTE = {\href{https://doi.org/10.1007/BF01351596}{DOI:10.1007/BF01351596}}, - VOLUME = {229}, - YEAR = {1977}, - NUMBER = {2}, - PAGES = {97--111}, - ISSN = {0025-5831}, - MRCLASS = {13H99 (14B10)}, - MRNUMBER = {0460317}, -MRREVIEWER = {J. A. Morrow}, - DOI = {10.1007/BF01351596}, - URL = {https://doi.org/10.1007/BF01351596}, -} - -@article {MR0491722, - AUTHOR = {Lipman, Joseph}, - TITLE = {Desingularization of two-dimensional schemes}, - JOURNAL = {Ann. Math. (2)}, - VOLUME = 107, - YEAR = 1978, - NOTE = {\href{https://doi.org/10.2307/1971141}{DOI:10.2307/1971141}}, - NUMBER = 2, - PAGES = {151--207}, - MRCLASS = {14J10}, - MRNUMBER = {0491722 (58 \#10924)}, - MRREVIEWER = {A. H. Wallace}, -} - -@article{MR0499299, - Author = {Hironaka, Heisuke}, - Fjournal = {Acta Mathematica Vietnamica}, - Issn = {0251-4184}, - Journal = {Acta Math. Vietnam.}, - Mrclass = {32C45}, - Mrnumber = {0499299 (58 \#17198)}, - Mrreviewer = {Tomas Sanchez Giralda}, - Number = 2, - Pages = {103--168}, - Title = {Bimeromorphic smoothing of a complex-analytic space}, - Volume = 2, - Year = 1977 -} - -@article{MR0799669, - Author = {Kobayashi, Ryoichi}, - Date-Added = {2015-06-19 15:12:21 +0000}, - Date-Modified ={2015-06-19 15:15:09 +0000}, - Journal = {Math. Ann.}, - Number = 3, - Pages = {385--398}, - Title = {Einstein-{K}ähler {V}-metrics on open {S}atake {V}-surfaces - with isolated quotient singularities}, - Note = - {\href{https://doi.org/10.1007/BF01455566}{DOI:10.1007/BF01455566}}, - Volume = 272, - Year = 1985 -} - -@article{MR0833802, - Author = {Cheng, Shiu-Yuen and Yau, Shing-Tung}, - Date-Added = {2015-06-19 12:18:15 +0000}, - Date-Modified ={2015-06-19 14:36:56 +0000}, - Journal = {Complex differential geometry and nonlinear differential - equations (Brunswick, Maine, 1984), Contemp. Math., - Amer. Math. Soc., Providence, RI}, - Pages = {31-44}, - Title = {Inequality between {C}hern numbers of singular {K}ähler - surfaces and characterization of orbit space of discrete group - of $SU(2,1)$}, - Volume = 49, - Year = 1986 -} - -@article{MR0944606, - Author = {Tsuji, Hajime}, - Date-Added = {2015-06-11 19:10:07 +0000}, - Date-Modified ={2015-06-11 19:11:40 +0000}, - Journal = {Math. Ann.}, - Number = 1, - Pages = {123-133}, - Title = {Existence and degeneration of Kähler-Einstein metrics on - minimal algebraic varieties of general type}, - Note = - {\href{https://doi.org/10.1007/BF01449219}{DOI:10.1007/BF01449219}}, - Volume = 281, - Year = 1988 -} - -@article{MR0976585, - Author = {Tsuji, Hajime}, - Date-Added = {2015-06-11 19:06:19 +0000}, - Date-Modified ={2015-06-11 19:08:01 +0000}, - Journal = {Topology}, - Number = 4, - Pages = {429-442}, - Title = {Stability of tangent bundles of minimal algebraic varieties.}, - Note = {\href{https://doi.org/10.1016/0040-9383(88)90022-5}{DOI:10.1016/0040-9383(88)90022-5}}, - Volume = 27, - Year = 1988 -} - -@book {MR1002324, - AUTHOR = {Serre, Jean-Pierre}, - TITLE = {Lectures on the {M}ordell-{W}eil theorem}, - SERIES = {Aspects of Mathematics, E15}, - NOTE = {Translated from the French and edited by Martin Brown from - notes by Michel - Waldschmidt. \href{https://doi.org/10.1007/978-3-663-14060-3}{DOI:10.1007/978-3-663-14060-3}}, - PUBLISHER = {Friedr. Vieweg \& Sohn, Braunschweig}, - YEAR = 1989, - PAGES = {x+218}, - ISBN = {3-528-08968-7}, - MRCLASS = {11G10 (11D41 11G30 14Gxx)}, - MRNUMBER = 1002324, - MRREVIEWER = {Joseph H. Silverman}, - URL = {https://doi.org/10.1007/978-3-663-14060-3}, -} - -@article {MR1030189, - AUTHOR = {Kobayashi, Ryoichi and Nakamura, Shu and Sakai, Fumio}, - TITLE = {A numerical characterization of ball quotients for normal - surfaces with branch loci}, - JOURNAL = {Proc. Japan Acad. Ser. A Math. Sci.}, - FJOURNAL = {Japan Academy. Proceedings. Series A. Mathematical Sciences}, - VOLUME = 65, - YEAR = 1989, - NOTE = {\href{http://projecteuclid.org/euclid.pja/1195512773}{euclid.pja/1195512773}.}, - NUMBER = 7, - PAGES = {238--241}, - ISSN = {0386-2194}, - MRCLASS = {32C10 (32J99 53C25 53C55)}, - MRNUMBER = 1030189, - MRREVIEWER = {Alan Michael Nadel}, - URL = {http://projecteuclid.org/euclid.pja/1195512773}, -} - -@article {MR1040197, - AUTHOR = {Simpson, Carlos T.}, - TITLE = {Harmonic bundles on noncompact curves}, - JOURNAL = {J. Amer. Math. Soc.}, - FJOURNAL = {Journal of the American Mathematical Society}, - VOLUME = 3, - YEAR = 1990, - Note = {\href{https://doi.org/10.2307/1990935}{DOI:10.2307/1990935}}, - NUMBER = 3, - PAGES = {713--770}, - ISSN = {0894-0347}, - MRCLASS = {58E20 (14C30 14H60 32G20)}, - MRNUMBER = 1040197, - MRREVIEWER = {N. J. Hitchin}, - DOI = {10.2307/1990935}, - URL = {https://doi.org/10.2307/1990935}, -} - -@book{MR1042981, - Address = {Redwood City, CA}, - Author = {Fulton, William}, - Isbn = {0-201-51010-3}, - Mrclass = {14Hxx (14-01)}, - Mrnumber = {1042981 (90k:14023)}, - Note = {An introduction to algebraic geometry, Notes written with the - collaboration of Richard Weiss, Reprint of 1969 - original. Freely available from the author's web site at - \url{http://www.math.lsa.umich.edu/~wfulton}.}, - Pages = {xxii+226}, - Publisher = {Addison-Wesley Publishing Company Advanced Book Program}, - Series = {Advanced Book Classics}, - Title = {Algebraic curves}, - Year = 1989 -} - -@incollection {MR1044586, - AUTHOR = {Knop, Friedrich and Kraft, Hanspeter and Vust, Thierry}, - TITLE = {The {P}icard group of a {$G$}-variety}, - BOOKTITLE = {Algebraische {T}ransformationsgruppen und - {I}nvariantentheorie}, - SERIES = {DMV Sem.}, - VOLUME = 13, - PAGES = {77--87}, - PUBLISHER = {Birkhäuser, Basel}, - YEAR = 1989, - MRCLASS = {14C22 (14D25 14L30)}, - MRNUMBER = 1044586, -} - -@book {MR1059457, - AUTHOR = {Gunning, Robert C.}, - TITLE = {Introduction to holomorphic functions of several variables. - {V}ol. {III}. Homological theory}, - SERIES = {The Wadsworth \& Brooks/Cole Mathematics Series}, - PUBLISHER = {Wadsworth \& Brooks/Cole Advanced Books \& Software, Monterey, - CA}, - YEAR = 1990, - PAGES = {xx+194}, - ISBN = {0-534-13310-X}, - MRCLASS = {32-01}, - MRNUMBER = 1059457, - MRREVIEWER = {Eric Bedford}, -} - -@article {MR1096125, - AUTHOR = {Vojta, Paul}, - TITLE = {On algebraic points on curves}, - JOURNAL = {Compositio Math.}, - FJOURNAL = {Compositio Mathematica}, - VOLUME = 78, - YEAR = 1991, - Note = - {\href{http://www.numdam.org/item/CM_1991__78_1_29_0}{numdam.CM-1991-78-1-29-0}}, - NUMBER = 1, - PAGES = {29--36}, - ISSN = {0010-437X}, - CODEN = {CMPMAF}, - MRCLASS = {11G30 (14H05)}, - MRNUMBER = 1096125, - MRREVIEWER = {I. V. Dolgachev}, - URL = {http://www.numdam.org/item?id=CM_1991__78_1_29_0}, -} - -@article {MR1096426, - AUTHOR = {Coleman, Robert F.}, - TITLE = {Manin's proof of the {M}ordell conjecture over function - fields}, - JOURNAL = {Enseign. Math. (2)}, - FJOURNAL = {L'Enseignement Mathématique. Revue Internationale. 2e Série}, - VOLUME = {36}, - YEAR = {1990}, - NUMBER = {3-4}, - PAGES = {393--427}, - ISSN = {0013-8584}, - MRCLASS = {11G30}, - MRNUMBER = {1096426}, -MRREVIEWER = {Joseph H. Silverman}, - Note = {\href{https://doi.org/10.5169/seals-57915}{DOI:10.5169/seals-57915}} -} - -@article {MR1106753, - AUTHOR = {Voloch, José F.}, - TITLE = {On the conjectures of {M}ordell and {L}ang in positive - characteristics}, - JOURNAL = {Invent. Math.}, - FJOURNAL = {Inventiones Mathematicae}, - VOLUME = 104, - YEAR = 1991, - NOTE = - {\href{https://doi.org/10.1007/BF01245094}{DOI:10.1007/BF01245094}}, - NUMBER = 3, - PAGES = {643--646}, - ISSN = {0020-9910}, - MRCLASS = {11G30 (14H25)}, - MRNUMBER = 1106753, - MRREVIEWER = {Joseph H. Silverman}, - URL = {https://doi.org/10.1007/BF01245094}, -} - -@article {MR1109353, - AUTHOR = {Faltings, Gerd}, - TITLE = {Diophantine approximation on abelian varieties}, - JOURNAL = {Ann. of Math. (2)}, - FJOURNAL = {Annals of Mathematics. Second Series}, - VOLUME = {133}, - YEAR = {1991}, - NUMBER = {3}, - PAGES = {549--576}, - ISSN = {0003-486X}, - MRCLASS = {11G10 (11J99)}, - MRNUMBER = {1109353}, -MRREVIEWER = {Joseph H. Silverman}, - DOI = {10.2307/2944319}, - URL = {https://doi.org/10.2307/2944319}, -} - -@article {MR1144433, - AUTHOR = {Schneider, Michael}, - TITLE = {Symmetric differential forms as embedding obstructions and - vanishing theorems}, - JOURNAL = {J. Algebraic Geom.}, - FJOURNAL = {Journal of Algebraic Geometry}, - VOLUME = {1}, - YEAR = {1992}, - NUMBER = {2}, - PAGES = {175--181}, - ISSN = {1056-3911}, - MRCLASS = {14F17}, - MRNUMBER = {1144433}, -MRREVIEWER = {Mei Chu Chang}, -} - -@article{MR1144434, - Author = {Kawamata, Yujiro}, - Fjournal = {Journal of Algebraic Geometry}, - Issn = {1056-3911}, - Journal = {J. Algebraic Geom.}, - Mrclass = {14D15 (14J40 32G05 32J18)}, - Mrnumber = {1144434 (93e:14016)}, - Mrreviewer = {Bruce Hunt}, - Number = 2, - Pages = {183--190}, - Title = {Unobstructed deformations. {A} remark on a paper of - {Z}. {R}an: ``{D}eformations of manifolds with torsion or - negative canonical bundle'' [{J}. {A}lgebraic {G}eom.\ {\bf 1} - (1992), no.\ 2, 279--291; {MR}1144440 (93e:14015)]}, - Volume = 1, - Year = 1992 -} - -@incollection {MR1145250, - AUTHOR = {Enoki, Ichiro}, - TITLE = {Compact {R}icci-flat {K}ähler manifolds}, - BOOKTITLE = {Kähler metric and moduli spaces}, - SERIES = {Adv. Stud. Pure Math.}, - VOLUME = 18, - PAGES = {229--256}, - PUBLISHER = {Academic Press, Boston, MA}, - YEAR = 1990, - MRCLASS = {53C25 (32J27 32L07 53C55)}, - MRNUMBER = 1145250, - MRREVIEWER = {Yang Lian Pan}, -} - -@article{MR1145268, - Author = {Sugiyama, Kenichi}, - Date-Added = {2015-06-19 14:43:30 +0000}, - Date-Modified ={2015-06-20 11:59:48 +0000}, - Journal = {Adv. Stud. Pure Math.}, - Pages = {417--433}, - Title = {Einstein-{K}ähler metrics on minimal varieties of general type - and an inequality between {C}hern numbers}, - Volume = {18-I}, - Year = 1990 -} - -@book {MR1153249, - AUTHOR = {Fulton, William and Harris, Joe}, - TITLE = {Representation theory. A first course}, - SERIES = {Graduate Texts in Mathematics}, - VOLUME = 129, - PUBLISHER = {Springer-Verlag, New York}, - YEAR = 1991, - PAGES = {xvi+551}, - ISBN = {0-387-97527-6; 0-387-97495-4}, - MRCLASS = {20G05 (17B10 20G20 22E46)}, - MRNUMBER = 1153249, - MRREVIEWER = {James E. Humphreys}, - NOTE = {\href{https://doi.org/10.1007/978-1-4612-0979-9}{DOI:10.1007/978-1-4612-0979-9}.}, - DOI = {10.1007/978-1-4612-0979-9}, - URL = {https://doi.org/10.1007/978-1-4612-0979-9}, -} - -@article{MR1157844, - Author = {Le Potier, Joseph}, - Fjournal = {Astérisque}, - Issn = {0303-1179}, - Journal = {Astérisque}, - Mrclass = {14C30 (14D07 14D20 32J25 53C07)}, - Mrnumber = {1157844 (93e:14012)}, - Mrreviewer = {Robert J. Fisher, Jr.}, - Note = {Séminaire Bourbaki, Vol. 1990/91}, - Number = {201-203}, - Pages = {Exp.\ No.\ 737, 221--268 (1992)}, - Title = {Fibrés de {H}iggs et systèmes locaux}, - Year = 1991 -} - -@inproceedings {MR1159261, - AUTHOR = {Simpson, Carlos T.}, - TITLE = {Nonabelian {H}odge theory}, - BOOKTITLE = {Proceedings of the {I}nternational {C}ongress of - {M}athematicians, {V}ol.\ {I}, {II} ({K}yoto, 1990)}, - PAGES = {747--756}, - PUBLISHER = {Math. Soc. Japan, Tokyo}, - YEAR = 1991, - MRCLASS = {14C30 (14J60 22E40 32J27 58D27)}, - MRNUMBER = {1159261 (93c:14010)}, - MRREVIEWER = {Richard M. Hain}, -} - -@book {MR1162108, - AUTHOR = {Fujita, Takao}, - TITLE = {Classification theories of polarized varieties}, - SERIES = {London Mathematical Society Lecture Note Series}, - VOLUME = {155}, - PUBLISHER = {Cambridge University Press, Cambridge}, - YEAR = {1990}, - PAGES = {xiv+205}, - ISBN = {0-521-39202-0}, - MRCLASS = {14C20 (14J40 14J60)}, - MRNUMBER = {1162108}, -MRREVIEWER = {Elvira Laura Livorni}, - NOTE = {\href{https://doi.org/10.1017/CBO9780511662638}{DOI:10.1017/CBO9780511662638}}, - DOI = {10.1017/CBO9780511662638}, - URL = {https://doi.org/10.1017/CBO9780511662638}, -} - -@article {MR1163733, - AUTHOR = {Tian, Gang}, - TITLE = {On stability of the tangent bundles of {F}ano varieties}, - JOURNAL = {Internat. J. Math.}, - FJOURNAL = {International Journal of Mathematics}, - VOLUME = {3}, - YEAR = {1992}, - NOTE = {\href{https://doi.org/10.1142/S0129167X92000175}{DOI:10.1142/S0129167X92000175}}, - NUMBER = {3}, - PAGES = {401--413}, - ISSN = {0129-167X}, - MRCLASS = {32L07 (14J45 53C25)}, - MRNUMBER = {1163733}, -MRREVIEWER = {Jaros\l aw A. Wi\'{s}niewski}, - DOI = {10.1142/S0129167X92000175}, - URL = {https://doi.org/10.1142/S0129167X92000175}, -} - -@article {MR1165352, - AUTHOR = {Semmes, Stephen}, - TITLE = {Complex {M}onge-{A}mpère and symplectic manifolds}, - JOURNAL = {Amer. J. Math.}, - FJOURNAL = {American Journal of Mathematics}, - VOLUME = {114}, - YEAR = {1992}, - NUMBER = {3}, - PAGES = {495--550}, - ISSN = {0002-9327}, - MRCLASS = {32F07 (35J60 58F05)}, - MRNUMBER = {1165352}, - NOTE = {\href{https://doi.org/10.2307/2374768}{DOI:10.2307/2374768}}, - DOI = {10.2307/2374768}, - URL = {https://doi.org/10.2307/2374768}, -} - -@article {MR1166957, - AUTHOR = {Borisov, Alexander A. and Borisov, Lev A.}, - TITLE = {Singular toric {F}ano varieties}, - JOURNAL = {Mat. Sb.}, - FJOURNAL = {Matematicheski\u{i} Sbornik}, - VOLUME = 183, - YEAR = 1992, - NOTE = {\href{https://doi.org/10.1070/SM1993v075n01ABEH003385}{DOI:10.1070/SM1993v075n01ABEH003385}}, - NUMBER = 2, - PAGES = {134--141}, - ISSN = {0368-8666}, - MRCLASS = {14J45 (14M25)}, - MRNUMBER = 1166957, - MRREVIEWER = {Yuri G. Prokhorov}, - DOI = {10.1070/SM1993v075n01ABEH003385}, - URL = {https://doi.org/10.1070/SM1993v075n01ABEH003385}, -} - -@book{MR1177168, - Author = {Katok, Svetlana}, - Isbn = {0-226-42582-7; 0-226-42583-5}, - Mrclass = {20H10 (30F35)}, - Mrnumber = {1177168 (93d:20088)}, - Mrreviewer = {I. Kra}, - Pages = {x+175}, - Publisher = {University of Chicago Press, Chicago, IL}, - Series = {Chicago Lectures in Mathematics}, - Title = {Fuchsian groups}, - Year = 1992 -} - -@article{MR1179076, - Author = {Simpson, Carlos T.}, - Coden = {PMIHA6}, - Fjournal = {Institut des Hautes Études Scientifiques. Publications - Mathématiques}, - Issn = {0073-8301}, - Journal = {Inst. Hautes Études Sci. Publ. Math.}, - Mrclass = {32G13 (14D07 53C07 58D27 58E15)}, - Mrnumber = {1179076 (94d:32027)}, - Mrreviewer = {William Goldman}, - Note = - {\href{https://doi.org/10.1007/BF02699491}{DOI:10.1007/BF02699491}, - \href{http://www.numdam.org/item?id=PMIHES_1992__75__5_0}{numdam.PMIHES-1992-75-5-0}}, - Pages = {5--95}, - Title = {Higgs bundles and local systems}, - Url = {http://www.numdam.org/item?id=PMIHES_1992__75__5_0}, - Volume = 75, - Year = 1992, - Bdsk-Url-1 = {http://www.numdam.org/item?id=PMIHES_1992__75__5_0} -} - -@book{MR1194180, - Address = {New York}, - Author = {Dimca, Alexandru}, - Doi = {10.1007/978-1-4612-4404-2}, - Isbn = {0-387-97709-0}, - Mrclass = {32Sxx (14J70 32S25 32S50 57M25 57R45 58C27)}, - Mrnumber = {1194180 (94b:32058)}, - Mrreviewer = {Aleksandr G. Aleksandrov}, - Pages = {xvi+263}, - Publisher = {Springer-Verlag}, - Series = {Universitext}, - Title = {Singularities and topology of hypersurfaces}, - Url = {https://doi.org/10.1007/978-1-4612-4404-2}, - Year = 1992, - Bdsk-Url-1 = {https://doi.org/10.1007/978-1-4612-4404-2} -} - -@article{MR1240585, - Author = {García-Prada, Oscar}, - Coden = {CMPHAY}, - Fjournal = {Communications in Mathematical Physics}, - Issn = {0010-3616}, - Journal = {Comm. Math. Phys.}, - Mrclass = {53C07 (32L07 58E15)}, - Mrnumber = {1240585 (95d:53024)}, - Mrreviewer = {Steven B. Bradlow}, - Number = 3, - Pages = {527--546}, - Title = {Invariant connections and vortices}, - Note = - {\href{http://projecteuclid.org/euclid.cmp/1104253716}{euclid.cmp/1104253716}}, - Url = {http://projecteuclid.org/euclid.cmp/1104253716}, - Volume = 156, - Year = 1993, - Bdsk-Url-1 = {http://projecteuclid.org/euclid.cmp/1104253716} -} - -@article {MR1253623, - AUTHOR = {Andreatta, Marco and Wiśniewski, Jarosław A.}, - TITLE = {A note on nonvanishing and applications}, - JOURNAL = {Duke Math. J.}, - FJOURNAL = {Duke Mathematical Journal}, - VOLUME = 72, - YEAR = 1993, - NOTE = - {\href{https://doi.org/10.1016/10.1215/S0012-7094-93-07228-6}{DOI:10.1215/S0012-7094-93-07228-6}. Preprint - \href{http://arxiv.org/abs/alg-geom/9302001}{arXiv:alg-geom/9302001}.}, - NUMBER = 3, - PAGES = {739--755}, - ISSN = {0012-7094}, - CODEN = {DUMJAO}, - MRCLASS = {14C20 (14D99)}, - MRNUMBER = {1253623 (95c:14007)}, - MRREVIEWER = {Andrew J. Sommese}, - DOI = {10.1215/S0012-7094-93-07228-6}, - URL = {https://doi.org/10.1215/S0012-7094-93-07228-6}, -} - -@inproceedings {MR1291023, - AUTHOR = {Hartshorne, Robin}, - TITLE = {Generalized divisors on {G}orenstein schemes}, - BOOKTITLE = {Proceedings of {C}onference on {A}lgebraic {G}eometry and {R}ing {T}heory in honor of {M}ichael {A}rtin, {P}art {III} ({A}ntwerp, 1992)}, - JOURNAL = {$K$-Theory}, - FJOURNAL = {$K$-Theory. An Interdisciplinary Journal for the Development, Application, and Influence of $K$-Theory in the Mathematical Sciences}, - VOLUME = {8}, - YEAR = {1994}, - NOTE = {\href{https://doi.org/10.1007/BF00960866}{DOI:10.1007/BF00960866}}, - NUMBER = {3}, - PAGES = {287--339}, - ISSN = {0920-3036}, - MRCLASS = {14C20 (14A15 14M06)}, - MRNUMBER = {1291023}, -MRREVIEWER = {G. Horrocks}, - DOI = {10.1007/BF00960866}, - URL = {https://doi.org/10.1007/BF00960866}, -} - -@article {MR1295591, - AUTHOR = {Gray, Jeremy}, - TITLE = {On the history of the {R}iemann mapping theorem}, - JOURNAL = {Rend. Circ. Mat. Palermo (2) Suppl.}, - FJOURNAL = {Rendiconti del Circolo Matematico di Palermo. Serie II. - Supplemento}, - NUMBER = 34, - YEAR = 1994, - PAGES = {47--94}, - MRCLASS = {30C35 (01A55)}, - MRNUMBER = 1295591, - MRREVIEWER = {D. H. Hamilton}, -} - -@article{MR1298542, - Author = {Gurjar, Rajendra V. and Zhang, De-Qi}, - Fjournal = {The University of Tokyo. Journal of Mathematical Sciences}, - Issn = {1340-5705}, - Journal = {J. Math. Sci. Univ. Tokyo}, - Mrclass = {14F35 (14E15 14J17)}, - Mrnumber = {1298542 (95m:14015)}, - Mrreviewer = {F. E. A. Johnson}, - Number = 1, - Pages = {137--180}, - Title = {{$\pi_1$} of smooth points of a log del {P}ezzo surface is - finite. {I}}, - Volume = 1, - Year = 1994 -} - -@article {MR1298994, - AUTHOR = {Alexeev, Valery}, - TITLE = {Boundedness and {$K^2$} for log surfaces}, - JOURNAL = {Internat. J. Math.}, - FJOURNAL = {International Journal of Mathematics}, - VOLUME = 5, - YEAR = 1994, - NOTE = {\href{https://doi.org/10.1142/S0129167X94000395}{DOI:10.1142/S0129167X94000395}}, - NUMBER = 6, - PAGES = {779--810}, - ISSN = {0129-167X}, - MRCLASS = {14J10 (14J25)}, - MRNUMBER = 1298994, - MRREVIEWER = {Mark Gross}, - DOI = {10.1142/S0129167X94000395}, - URL = {https://doi.org/10.1142/S0129167X94000395}, -} - -@book{MR1304906, - Address = {Berlin}, - Author = {Mumford, David and Fogarty, John and Kirwan, Frances}, - Doi = {10.1007/978-3-642-57916-5}, - Edition = {Third}, - Isbn = {3-540-56963-4}, - Mrclass = {14D25 (58E05 58F05)}, - Mrnumber = {1304906 (95m:14012)}, - Mrreviewer = {Yi Hu}, - NOTE = {\href{https://doi.org/10.1007/978-3-642-57916-5}{DOI:10.1007/978-3-642-57916-5}}, - Pages = {xiv+292}, - Publisher = {Springer-Verlag}, - Series = {Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results - in Mathematics and Related Areas (2)]}, - Title = {Geometric invariant theory}, - Url = {https://doi.org/10.1007/978-3-642-57916-5}, - Volume = 34, - Year = 1994, - Bdsk-Url-1 = {https://doi.org/10.1007/978-3-642-57916-5} -} - -@article{MR1307297, - Author = {Simpson, Carlos T.}, - Coden = {PMIHA6}, - Fjournal = {Institut des Hautes Études Scientifiques. Publications - Mathématiques}, - Issn = {0073-8301}, - Journal = {Inst. Hautes Études Sci. Publ. Math.}, - Note = - {\href{http://www.numdam.org/item/PMIHES_1994__79__47_0}{numdam.PMIHES_1994__79__47_0}}, - Mrclass = {14D20 (14D22 14D25 14F05)}, - Mrnumber = {1307297 (96e:14012)}, - Mrreviewer = {Nitin Nitsure}, - Pages = {47--129}, - Title = {Moduli of representations of the fundamental group of a smooth - projective variety. {I}}, - Url = {http://www.numdam.org/item?id=PMIHES_1994__79__47_0}, - Volume = 79, - Year = 1994, - Bdsk-Url-1 = {http://www.numdam.org/item?id=PMIHES_1994__79__47_0} -} - -@article{MR1320603, - Author = {Simpson, Carlos T.}, - Coden = {PMIHA6}, - Fjournal = {Institut des Hautes Études Scientifiques. Publications - Mathématiques}, - Issn = {0073-8301}, - Journal = {Inst. Hautes Études Sci. Publ. Math.}, - Note = - {\href{http://www.numdam.org/item/PMIHES_1994__80__5_0}{numdam.PMIHES_1994__80__5_0}}, - Mrclass = {14D20 (14D22 14F05 14F10)}, - Mrnumber = {1320603 (96e:14013)}, - Mrreviewer = {Nitin Nitsure}, - Pages = {5--79 (1995)}, - Title = {Moduli of representations of the fundamental group of a smooth - projective variety. {II}}, - Url = {http://www.numdam.org/item?id=PMIHES_1994__80__5_0}, - Volume = 80, - Year = 1994, - Bdsk-Url-1 = {http://www.numdam.org/item?id=PMIHES_1994__80__5_0} -} - -@book {MR1324108, - AUTHOR = {Narasimhan, Raghavan}, - TITLE = {Several complex variables}, - SERIES = {Chicago Lectures in Mathematics}, - NOTE = {Reprint of the 1971 original}, - PUBLISHER = {University of Chicago Press, Chicago, IL}, - YEAR = 1995, - PAGES = {x+174}, - ISBN = {0-226-56817-2}, - MRCLASS = {32-01}, - MRNUMBER = 1324108, -} - -@incollection {MR1326618, - AUTHOR = {Remmert, Reinhold}, - TITLE = {Local theory of complex spaces}, - BOOKTITLE = {Several complex variables, {VII}}, - SERIES = {Encyclopaedia Math. Sci.}, - VOLUME = {74}, - PAGES = {7--96}, - PUBLISHER = {Springer, Berlin}, - YEAR = {1994}, - MRCLASS = {32C15 (32B05 32C20)}, - MRNUMBER = {1326618}, - DOI = {10.1007/978-3-662-09873-8\_2}, - URL = {https://doi.org/10.1007/978-3-662-09873-8_2}, - Note = {\href{https://doi.org/10.1007/978-3-662-09873-8_2}{DOI:10.1007/978-3-662-09873-8\_2}} -} - -@incollection {MR1326619, - AUTHOR = {Peternell, Thomas and Remmert, Reinhold}, - TITLE = {Differential calculus, holomorphic maps and linear structures on complex spaces}, - BOOKTITLE = {Several complex variables, {VII}}, - NOTE = {\href{https://doi.org/10.1007/978-3-662-09873-8_8}{DOI:10.1007/978-3-662-09873-8\_8}}, - SERIES = {Encyclopaedia Math. Sci.}, - VOLUME = {74}, - PAGES = {97--144}, - PUBLISHER = {Springer, Berlin}, - YEAR = {1994}, - MRCLASS = {32C35 (32C37 32L05)}, - MRNUMBER = {1326619}, - DOI = {10.1007/978-3-662-09873-8\_3}, - URL = {https://doi.org/10.1007/978-3-662-09873-8_3}, -} - -@incollection {MR1326624, - AUTHOR = {Peternell, Thomas}, - TITLE = {Modifications}, - BOOKTITLE = {Several complex variables, {VII}}, - SERIES = {Encyclopaedia Math. Sci.}, - VOLUME = 74, - PAGES = {285--317}, - PUBLISHER = {Springer, Berlin}, - YEAR = 1994, - MRCLASS = {32S45 (32J20)}, - MRNUMBER = 1326624, - NOTE = {\href{https://doi.org/10.1007/978-3-662-09873-8_8}{DOI:10.1007/978-3-662-09873-8\_8}}, - DOI = {10.1007/978-3-662-09873-8_8}, - URL = {https://doi.org/10.1007/978-3-662-09873-8_8}, -} - -@incollection{MR1326625, - Address = {Berlin}, - Author = {Campana, F. and Peternell, Th.}, - Booktitle = {Several complex variables, {VII}}, - Mrclass = {32G10 (32F10)}, - Mrnumber = 1326625, - Pages = {319--349}, - Publisher = {Springer}, - Series = {Encyclopaedia Math. Sci.}, - Title = {Cycle spaces}, - Volume = 74, - Year = 1994 -} - -@book {MR1328834, - AUTHOR = {Shafarevich, Igor R.}, - TITLE = {Basic algebraic geometry. 2}, - EDITION = {Second}, - NOTE = {Schemes and complex manifolds, Translated from the 1988 Russian edition by Miles Reid. \href{https://doi.org/10.1007/978-3-642-57956-1}{DOI:10.1007/978-3-642-57956-1}}, - PUBLISHER = {Springer-Verlag, Berlin}, - YEAR = 1994, - PAGES = {xiv+269}, - ISBN = {3-540-57554-5}, - MRCLASS = {14-01}, - MRNUMBER = 1328834, -} - -@book {MR1334091, - AUTHOR = {Akhiezer, Dmitri N.}, - TITLE = {Lie group actions in complex analysis}, - SERIES = {Aspects of Mathematics, E27}, - PUBLISHER = {Friedr. Vieweg \& Sohn, Braunschweig}, - YEAR = {1995}, - PAGES = {viii+201}, - ISBN = {3-528-06420-X}, - MRCLASS = {32M05 (22-02 22E10 32M10)}, - MRNUMBER = {1334091}, -MRREVIEWER = {B. Gilligan}, - NOTE = {\href{https://doi.org/10.1007/978-3-322-80267-5}{DOI:10.1007/978-3-322-80267-5}}, - DOI = {10.1007/978-3-322-80267-5}, - URL = {https://doi.org/10.1007/978-3-322-80267-5}, -} - -@book {MR1335917, - AUTHOR = {Hirzebruch, Friedrich}, - TITLE = {Topological methods in algebraic geometry}, - SERIES = {Classics in Mathematics}, - NOTE = {Translated from the German and Appendix One by R. L. E. - Schwarzenberger, With a preface to the third English edition - by the author and Schwarzenberger, Appendix Two by A. Borel, - Reprint of the 1978 edition}, - PUBLISHER = {Springer-Verlag, Berlin}, - YEAR = 1995, - PAGES = {xii+234}, - ISBN = {3-540-58663-6}, - MRCLASS = {57-02 (01A75 14-02)}, - MRNUMBER = 1335917, -} - -@article {MR1340353, - AUTHOR = {Andreatta, Marco}, - TITLE = {Some remarks on the study of good contractions}, - JOURNAL = {Manuscripta Math.}, - FJOURNAL = {Manuscripta Mathematica}, - VOLUME = 87, - YEAR = 1995, - NOTE = - {\href{https://doi.org/10.1007/BF02570480}{DOI:10.1007/BF02570480}.}, - NUMBER = 3, - PAGES = {359--367}, - ISSN = {0025-2611}, - CODEN = {MSMHB2}, - MRCLASS = {14E30}, - MRNUMBER = {1340353 (96i:14017)}, - MRREVIEWER = {Mark Gross}, - DOI = {10.1007/BF02570480}, - URL = {https://doi.org/10.1007/BF02570480}, -} - -@book {MR1341589, - AUTHOR = {Kollár, János}, - TITLE = {Shafarevich maps and automorphic forms}, - SERIES = {M. B. Porter Lectures}, - PUBLISHER = {Princeton University Press, Princeton, NJ}, - YEAR = 1995, - PAGES = {x+201}, - ISBN = {0-691-04381-7}, - MRCLASS = {14E20 (14J10 14J15 32J18 32N10)}, - MRNUMBER = {1341589 (96i:14016)}, - MRREVIEWER = {Kang Zuo}, - NOTE = {\href{https://doi.org/10.1515/9781400864195}{DOI:10.1515/9781400864195}}, - DOI = {10.1515/9781400864195}, - URL = {https://doi.org/10.1515/9781400864195}, -} - -@article {MR1358040, - AUTHOR = {Barth, Wolf}, - TITLE = {Two projective surfaces with many nodes, admitting the symmetries of the icosahedron}, - JOURNAL = {J. 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[Crelle's Journal]}, - VOLUME = {472}, - YEAR = {1996}, - PAGES = {139--156}, - ISSN = {0075-4102}, - MRCLASS = {32J27 (14D07 32J25 58E20)}, - MRNUMBER = {1384908}, -MRREVIEWER = {Kimio Miyajima}, - NOTE = {\href{https://doi.org/10.1515/crll.1996.472.139}{DOI:10.1515/crll.1996.472.139}}, - DOI = {10.1515/crll.1996.472.139}, - URL = {https://doi.org/10.1515/crll.1996.472.139}, -} - -@book {MR1393940, - AUTHOR = {Kobayashi, Shoshichi and Nomizu, Katsumi}, - TITLE = {Foundations of differential geometry. {V}ol. {I}}, - SERIES = {Wiley Classics Library}, - NOTE = {Reprint of the 1963 original}, - PUBLISHER = {John Wiley \& Sons, Inc., New York}, - YEAR = 1996, - PAGES = {xii+329}, - ISBN = {0-471-15733-3}, - MRCLASS = {53-01}, - MRNUMBER = 1393940, -} - -@book {MR1393941, - AUTHOR = {Kobayashi, Shoshichi and Nomizu, Katsumi}, - TITLE = {Foundations of differential geometry. {V}ol. {II}}, - SERIES = {Wiley Classics Library}, - NOTE = {Reprint of the 1969 original}, - PUBLISHER = {John Wiley \& Sons, Inc., New York}, - YEAR = 1996, - PAGES = {xvi+468}, - ISBN = {0-471-15732-5}, - MRCLASS = {53-01}, - MRNUMBER = 1393941, -} - -@book{MR1406314, - Address = {Cambridge}, - Author = {Beauville, Arnaud}, - Doi = {10.1017/CBO9780511623936}, - Edition = {Second}, - Isbn = {0-521-49510-5; 0-521-49842-2}, - Mrclass = {14Jxx (14-02)}, - Mrnumber = {1406314 (97e:14045)}, - Note = {Translated from the 1978 French original by R. Barlow, with assistance from N. I. Shepherd-Barron and M. Reid}, - Pages = {x+132}, - Publisher = {Cambridge University Press}, - Series = {London Mathematical Society Student Texts}, - Title = {Complex algebraic surfaces}, - Url = {https://doi.org/10.1017/CBO9780511623936}, - Volume = 34, - Year = 1996, - Bdsk-Url-1 = {https://doi.org/10.1017/CBO9780511623936} -} - -@article {MR1420223, - AUTHOR = {Shokurov, Vyacheslav V.}, - TITLE = {{$3$}-fold log models}, - NOTE = {Algebraic geometry, 4. \href{https://doi.org/10.1007/BF02362335}{DOI:10.1007/BF02362335}}, - JOURNAL = {J. Math. Sci.}, - FJOURNAL = {Journal of Mathematical Sciences}, - VOLUME = 81, - YEAR = 1996, - NUMBER = 3, - PAGES = {2667--2699}, - ISSN = {1072-3374}, - MRCLASS = {14E30 (14E15 14E35)}, - MRNUMBER = 1420223, - MRREVIEWER = {Alessio Corti}, - DOI = {10.1007/BF02362335}, - URL = {https://doi.org/10.1007/BF02362335}, -} - -@article {MR1421952, - AUTHOR = {Esnault, Hélène}, - TITLE = {Recent developments on characteristic classes of flat bundles - on complex algebraic manifolds}, - JOURNAL = {Jahresber. Deutsch. Math.-Verein.}, - FJOURNAL = {Jahresbericht der Deutschen Mathematiker-Vereinigung}, - VOLUME = 98, - YEAR = 1996, - NUMBER = 4, - PAGES = {182--191}, - ISSN = {0012-0456}, - CODEN = {JDMVA7}, - MRCLASS = {14C25 (14F40 32J25 57R20)}, - MRNUMBER = 1421952, - MRREVIEWER = {I. Dolgachev}, -} - -@article {MR1422313, - AUTHOR = {Biquard, Olivier}, - TITLE = {Fibrés de {H}iggs et connexions intégrables: le cas logarithmique (diviseur lisse)}, - JOURNAL = {Ann. Sci. École Norm. Sup. 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Quatrième Série}, - VOLUME = 30, - YEAR = 1997, - Note = {\href{https://doi.org/10.1016/S0012-9593(97)89915-6}{DOI:10.1016/S0012-9593(97)89915-6}}, - NUMBER = 1, - PAGES = {41--96}, - ISSN = {0012-9593}, - CODEN = {ASENAH}, - MRCLASS = {32L07 (14J60)}, - MRNUMBER = 1422313, - MRREVIEWER = {Nitin Nitsure}, - DOI = {10.1016/S0012-9593(97)89915-6}, - URL = {https://doi.org/10.1016/S0012-9593(97)89915-6}, -} - -@article {MR1436743, - AUTHOR = {Kim, Minhyong}, - TITLE = {Geometric height inequalities and the {K}odaira-{S}pencer map}, - JOURNAL = {Compositio Math.}, - FJOURNAL = {Compositio Mathematica}, - VOLUME = 105, - YEAR = 1997, - NOTE = - {\href{https://doi.org/10.1023/A:1017995416618}{DOI:A:1017995416618}}, - NUMBER = 1, - PAGES = {43--54}, - ISSN = {0010-437X}, - CODEN = {CMPMAF}, - MRCLASS = {14G25 (14D10 14H25)}, - MRNUMBER = {1436743 (98j:14029)}, - MRREVIEWER = {Atsushi Moriwaki}, - DOI = {10.1023/A:1017995416618}, - URL = {https://doi.org/10.1023/A:1017995416618}, -} - -@book {MR1441541, - AUTHOR = {Eberlein, Patrick B.}, - TITLE = {Geometry of nonpositively curved manifolds}, - SERIES = {Chicago Lectures in Mathematics}, - PUBLISHER = {University of Chicago Press, Chicago, IL}, - YEAR = {1996}, - PAGES = {vii+449}, - ISBN = {0-226-18197-9; 0-226-18198-7}, - MRCLASS = {53-02 (53C20 53C21 53C35)}, - MRNUMBER = {1441541}, -MRREVIEWER = {Mar\'{\i}a J. 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Algebraic Geom.}, - FJOURNAL = {Journal of Algebraic Geometry}, - VOLUME = {6}, - YEAR = {1997}, - NUMBER = {1}, - PAGES = {151--168}, - ISSN = {1056-3911}, - MRCLASS = {14J17 (14N10 94B05)}, - MRNUMBER = {1486992}, -MRREVIEWER = {Susan J. Colley}, -} - -@article{MR1487238, - Author = {Kawamata, Yujiro}, - Fjournal = {Journal of Algebraic Geometry}, - Issn = {1056-3911}, - Journal = {J. Algebraic Geom.}, - Mrclass = {14D15 (14J40 32G05 32J18)}, - Mrnumber = {1487238 (98k:14009)}, - Mrreviewer = {Bruce Hunt}, - Number = 4, - Pages = {803--804}, - Title = {Erratum on: ``{U}nobstructed deformations. {A} remark on a - paper of {Z}. {R}an: `{D}eformations of manifolds with torsion - or negative canonical bundle'\,'' [{J}. {A}lgebraic {G}eom.\ - {\bf 1} (1992), no.\ 2, 183--190; {MR}1144434 (93e:14016)]}, - Volume = 6, - Year = 1997 -} - -@article {MR1489117, - AUTHOR = {Namikawa, Yoshinori}, - TITLE = {Smoothing {F}ano {$3$}-folds}, - JOURNAL = {J. Algebraic Geom.}, - FJOURNAL = {Journal of Algebraic Geometry}, - VOLUME = {6}, - YEAR = {1997}, - NUMBER = {2}, - PAGES = {307--324}, - ISSN = {1056-3911}, - MRCLASS = {14J45 (14B07 14B12 14D15)}, - MRNUMBER = {1489117}, -MRREVIEWER = {Yuri G. Prokhorov}, -} - -@article {MR1510165, - AUTHOR = {Lindemann, Ferdinand}, - TITLE = {Ueber die {Z}ahl $\pi$}, - JOURNAL = {Math. Ann.}, - FJOURNAL = {Mathematische Annalen}, - VOLUME = {20}, - YEAR = {1882}, - NUMBER = {2}, - PAGES = {213--225}, - ISSN = {0025-5831}, - MRCLASS = {DML}, - Note = {\href{https://doi.org/10.1007/BF01446522}{DOI:10.1007/BF01446522}}, - MRNUMBER = {1510165}, - DOI = {10.1007/BF01446522}, - URL = {https://doi.org/10.1007/BF01446522}, -} - -@article {MR1512302, - AUTHOR = {Hermann, Grete}, - TITLE = {Die {F}rage der endlich vielen {S}chritte in der {T}heorie der {P}olynomideale}, - JOURNAL = {Math. Ann.}, - FJOURNAL = {Mathematische Annalen}, - VOLUME = {95}, - YEAR = {1926}, - NUMBER = {1}, - NOTE = {\href{https://doi.org/10.1007/BF01206635}{DOI:10.1007/BF01206635}}, - PAGES = {736--788}, - ISSN = {0025-5831}, - MRCLASS = {DML}, - MRNUMBER = {1512302}, - DOI = {10.1007/BF01206635}, - URL = {https://doi.org/10.1007/BF01206635}, -} - -@article {MR1581526, - AUTHOR = {Witt, Ernst}, - TITLE = {Zyklische {K}örper und {A}lgebren der {C}harakteristik {$p$} - vom {G}rad {$p^n$}. {S}truktur diskret bewerteter perfekter - {K}örper mit vollkommenem {R}estklassenkörper der - {C}harakteristik {$p$}}, - JOURNAL = {J. Reine Angew. Math.}, - FJOURNAL = {Journal für die Reine und Angewandte Mathematik. [Crelle's - Journal]}, - VOLUME = {176}, - YEAR = {1937}, - PAGES = {126--140}, - ISSN = {0075-4102}, - MRCLASS = {DML}, - MRNUMBER = {1581526}, - Note = {\href{https://doi.org/10.1515/crll.1937.176.126}{DOI:10.1515/crll.1937.176.126}}, - DOI = {10.1515/crll.1937.176.126}, - URL = {https://doi.org/10.1515/crll.1937.176.126}, -} - -@incollection {MR1603624, - AUTHOR = {Tian, Gang}, - TITLE = {Kähler-{E}instein metrics on algebraic manifolds}, - BOOKTITLE = {Transcendental methods in algebraic geometry ({C}etraro, - 1994)}, - SERIES = {Lecture Notes in Math.}, - VOLUME = 1646, - PAGES = {143--185}, - PUBLISHER = {Springer, Berlin}, - YEAR = 1996, - MRCLASS = {32L07 (53C25 53C55)}, - MRNUMBER = 1603624, - MRREVIEWER = {Thalia D. Jeffres}, - NOTE = - {\href{https://doi.org/10.1007/BFb0094304}{DOI:10.1007/BFb0094304}.}, - DOI = {10.1007/BFb0094304}, - URL = {https://doi.org/10.1007/BFb0094304}, -} - -@article {MR1618325, - AUTHOR = {Ko{\l}odziej, Sławomir}, - TITLE = {The complex {M}onge-{A}mpère equation}, - JOURNAL = {Acta Math.}, - FJOURNAL = {Acta Mathematica}, - VOLUME = 180, - YEAR = 1998, - NUMBER = 1, - Note = - {\href{https://doi.org/10.1007/BF02392879}{DOI:10.1007/BF02392879}}, - PAGES = {69--117}, - ISSN = {0001-5962}, - CODEN = {ACMAA8}, - MRCLASS = {32F07 (32C17 35J60)}, - MRNUMBER = 1618325, - MRREVIEWER = {M. Klimek}, - DOI = {10.1007/BF02392879}, - URL = {https://doi.org/10.1007/BF02392879}, -} - -@article {MR1646046, - AUTHOR = {Kawamata, Yujiro}, - TITLE = {Subadjunction of log canonical divisors. {II}}, - JOURNAL = {Amer. J. Math.}, - FJOURNAL = {American Journal of Mathematics}, - VOLUME = {120}, - YEAR = {1998}, - NOTE = {URL \url{http://muse.jhu.edu/journals/american_journal_of_mathematics/v120/120.5kawamata.pdf}}, - NUMBER = {5}, - PAGES = {893--899}, - ISSN = {0002-9327}, - MRCLASS = {14E30 (14J10)}, - MRNUMBER = {1646046}, -MRREVIEWER = {Alessio Corti}, - URL = {http://muse.jhu.edu/journals/american_journal_of_mathematics/v120/120.5kawamata.pdf}, -} - -@incollection {MR1668579, - AUTHOR = {Iskovskih, Vasily A. and Prokhorov, Yuri G.}, - TITLE = {Fano varieties}, - BOOKTITLE = {Algebraic geometry, {V}}, - SERIES = {Encyclopaedia Math. Sci.}, - VOLUME = {47}, - PAGES = {1--247}, - PUBLISHER = {Springer, Berlin}, - YEAR = {1999}, - MRCLASS = {14J45 (14E07 14F22 14K30)}, - MRNUMBER = {1668579}, -MRREVIEWER = {Takao Fujita}, -} - -@article {MR1691481, - AUTHOR = {Nakayama, Noboru}, - TITLE = {Projective algebraic varieties whose universal covering spaces are biholomorphic to {${\bf C}^n$}}, - JOURNAL = {J. Math. Soc. Japan}, - FJOURNAL = {Journal of the Mathematical Society of Japan}, - VOLUME = 51, - YEAR = 1999, - NUMBER = 3, - PAGES = {643--654}, - ISSN = {0025-5645}, - CODEN = {NISUBC}, - MRCLASS = {14E30 (14E20 14J10)}, - MRNUMBER = 1691481, - MRREVIEWER = {Azniv Kasparian}, - DOI = {10.2969/jmsj/05130643}, - URL = {https://doi.org/10.2969/jmsj/05130643}, -} - -@incollection {MR1715587, - AUTHOR = {Nakayama, Noboru}, - TITLE = {Normalized tautological divisors of semi-stable vector bundles}, - NOTE = {Free resolutions of coordinate rings of projective varieties and related topics (Japanese) (Kyoto, 1998), available on the internet at \url{http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/1078.html}}, - JOURNAL = {S\={u}rikaisekikenky\={u}sho K\B{o}ky\={u}roku}, - FJOURNAL = {S\={u}rikaisekikenky\={u}sho K\B{o}ky\={u}roku}, - NUMBER = {1078}, - YEAR = {1999}, - PAGES = {167--173}, - MRCLASS = {14J60 (14C20)}, - MRNUMBER = {1715587}, -MRREVIEWER = {Atsushi Noma}, -} - -@book {MR1738433, - AUTHOR = {Zuo, Kang}, - TITLE = {Representations of fundamental groups of algebraic varieties}, - SERIES = {Lecture Notes in Mathematics}, - VOLUME = {1708}, - PUBLISHER = {Springer-Verlag, Berlin}, - YEAR = {1999}, - PAGES = {viii+135}, - ISBN = {3-540-66312-6}, - MRCLASS = {14F35 (14E20 32J27 58E20)}, - MRNUMBER = {1738433}, - NOTE = {\href{https://doi.org/10.1007/BFb0092569}{DOI:10.1007/BFb0092569}}, - DOI = {10.1007/BFb0092569}, - URL = {https://doi.org/10.1007/BFb0092569}, -} - -@book {MR1747010, - AUTHOR = {Morosawa, Shunsuke and Nishimura, Yasuichiro and Taniguchi, - Masahiko and Ueda, Tetsuo}, - TITLE = {Holomorphic dynamics}, - SERIES = {Cambridge Studies in Advanced Mathematics}, - VOLUME = 66, - NOTE = {Translated from the 1995 Japanese original and revised by the - authors}, - PUBLISHER = {Cambridge University Press, Cambridge}, - YEAR = 2000, - PAGES = {xii+338}, - ISBN = {0-521-66258-3}, - MRCLASS = {37Fxx (30D05 32H50 32U35)}, - MRNUMBER = 1747010, - MRREVIEWER = {Estela A. Gavosto}, -} - -@incollection{MR1756407, - Author = {Vinberg, Ernest B. and Gorbatsevich, Vladimir V. and - Shvartsman, Ossip V.}, - Booktitle = {Lie groups and {L}ie algebras, {II}}, - Mrclass = {22E40}, - Mrnumber = 1756407, - Pages = {1--123, 217--223}, - Publisher = {Springer, Berlin}, - Series = {Encyclopaedia Math. Sci.}, - Title = {Discrete subgroups of {L}ie groups}, - Volume = 21, - Year = 2000 -} - -@article {MR1757883, - AUTHOR = {Kim, Minhyong}, - TITLE = {Erratum for: ``{G}eometric height inequalities and the - {K}odaira-{S}pencer map'' [{C}ompositio {M}ath. {\bf 105} - (1997), no. 1, 43--54; {MR}1436743 (98j:14029)]}, - JOURNAL = {Compositio Math.}, - FJOURNAL = {Compositio Mathematica}, - VOLUME = 121, - YEAR = 2000, - NOTE = - {\href{https://doi.org/10.1023/A:1001882724260}{DOI:A:1001882724260}}, - NUMBER = 2, - PAGES = 219, - ISSN = {0010-437X}, - CODEN = {CMPMAF}, - MRCLASS = {14G25 (14D10 14H25)}, - MRNUMBER = 1757883, - DOI = {10.1023/A:1001882724260}, - URL = {https://doi.org/10.1023/A:1001882724260}, -} - -@article {MR1758581, - AUTHOR = {Druel, Stéphane}, - TITLE = {Variétés algébriques dont le fibré tangent est totalement décomposé}, - JOURNAL = {J. Reine Angew. Math.}, - FJOURNAL = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]}, - VOLUME = {522}, - YEAR = {2000}, - PAGES = {161--171}, - ISSN = {0075-4102}, - MRCLASS = {14J40}, - MRNUMBER = {1758581}, -MRREVIEWER = {Takao Fujita}, - NOTE = {\href{https://doi.org/10.1515/crll.2000.036}{DOI:10.1515/crll.2000.036}. Preprint \href{https://arXiv.org/abs/math/9901138}{arXiv:math/9901138}}, - DOI = {10.1515/crll.2000.036}, - URL = {https://doi.org/10.1515/crll.2000.036}, -} - -@incollection{MR1760872, - Address = {Berlin}, - Author = {Beauville, Arnaud}, - Booktitle = {Complex analysis and algebraic geometry}, - Mrclass = {32J27 (32J15 32J18 32Q20)}, - Mrnumber = {1760872 (2001f:32030)}, - Mrreviewer = {Matthew B. Stenzel}, - Pages = {61--70}, - Publisher = {de Gruyter}, - Title = {Complex manifolds with split tangent bundle}, - Year = 2000, - Note = {\href{https://doi.org/10.1515/9783110806090}{DOI:10.1515/9783110806090}. \href{https://arxiv.org/abs/math/9809033}{arXiv:math/9809033}} -} - -@book {MR1761696, - AUTHOR = {Lemmermeyer, Franz}, - TITLE = {Reciprocity laws}, - SERIES = {Springer Monographs in Mathematics}, - NOTE = {From Euler to Eisenstein. \href{https://doi.org/10.1007/978-3-662-12893-0}{DOI:10.1007/978-3-662-12893-0}}, - PUBLISHER = {Springer-Verlag, Berlin}, - YEAR = {2000}, - PAGES = {xx+487}, - ISBN = {3-540-66957-4}, - MRCLASS = {11A15 (11L05 11R04 11R18)}, - MRNUMBER = {1761696}, -MRREVIEWER = {Charles Helou}, - DOI = {10.1007/978-3-662-12893-0}, - URL = {https://doi.org/10.1007/978-3-662-12893-0}, -} - -@article {MR1771144, - AUTHOR = {Kollár, János and Miyaoka, Yoichi and Mori, Shigefumi and Takagi, Hiromichi}, - TITLE = {Boundedness of canonical {$\bold Q$}-{F}ano 3-folds}, - JOURNAL = {Proc. Japan Acad. Ser. A Math. Sci.}, - FJOURNAL = {Japan Academy. Proceedings. Series A. Mathematical Sciences}, - VOLUME = {76}, - YEAR = {2000}, - NOTE = {\href{http://projecteuclid.org/getRecord?id=euclid.pja/1148393517}{euclid.pja/1148393517}}, - NUMBER = {5}, - PAGES = {73--77}, - ISSN = {0386-2194}, - MRCLASS = {14J45 (14E30)}, - MRNUMBER = {1771144}, -MRREVIEWER = {Yuri G. 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Math. Sci. (New York)}, - FJOURNAL = {Journal of Mathematical Sciences (New York)}, - VOLUME = {102}, - YEAR = {2000}, - NUMBER = {2}, - PAGES = {3876--3932}, - ISSN = {1072-3374}, - MRCLASS = {14E30 (14J26 14J30)}, - MRNUMBER = {1794169}, -MRREVIEWER = {I. Dolgachev}, - DOI = {10.1007/BF02984106}, - URL = {https://doi.org/10.1007/BF02984106}, -} - -@article {MR1815399, - AUTHOR = {Kim, Minhyong and Thakur, Dinesh S. and Voloch, José F.}, - TITLE = {Diophantine approximation and deformation}, - JOURNAL = {Bull. Soc. Math. France}, - FJOURNAL = {Bulletin de la Société Mathématique de France}, - VOLUME = 128, - YEAR = 2000, - NOTE = {\href{https://doi.org/10.24033/bsmf.2383}{DOI:10.24033/bsmf.2383}}, - NUMBER = 4, - PAGES = {585--598}, - ISSN = {0037-9484}, - MRCLASS = {11J61 (11G50 11J68 14D10)}, - MRNUMBER = 1815399, - MRREVIEWER = {Alain Lasjaunias}, - URL = {http://www.numdam.org/item?id=BSMF_2000__128_4_585_0}, -} - -@article {MR1819886, - AUTHOR = {Namikawa, Yoshinori}, - TITLE = {Deformation theory of singular symplectic {$n$}-folds}, - JOURNAL = {Math. 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Publ., River Edge, NJ}, - YEAR = {2002}, - MRCLASS = {32G05 (14P05)}, - MRNUMBER = {1945361}, -MRREVIEWER = {I. Dolgachev}, - NOTE = {\href{https://doi.org/10.1142/9789812777416_0009}{DOI:10.1142/9789812777416\_0009}. Preprint \href{https://arxiv.org/abs/math/0111245}{arXiv:math/0111245}}, - DOI = {10.1142/9789812777416_0009}, - URL = {https://doi.org/10.1142/9789812777416_0009}, -} - -@incollection{MR1954067, - Address = {Berlin}, - Author = {Langer, Adrian}, - Booktitle = {Algebraic geometry}, - Mrclass = {14J60 (14C20)}, - Mrnumber = {1954067 (2004b:14077)}, - Mrreviewer = {Gábor Megyesi}, - Pages = {237--256}, - Publisher = {de Gruyter}, - Title = {A note on {B}ogomolov's instability and {H}iggs sheaves}, - Year = 2002 -} - -@inproceedings {MR1957061, - AUTHOR = {Reid, Miles}, - TITLE = {Update on 3-folds}, - BOOKTITLE = {Proceedings of the {I}nternational {C}ongress of {M}athematicians, {V}ol. {II} ({B}eijing, 2002)}, - PAGES = {513--524}, - PUBLISHER = {Higher Ed. Press, Beijing}, - YEAR = 2002, - MRCLASS = {14J30 (14E30 14J32)}, - MRNUMBER = 1957061, - MRREVIEWER = {A. S. Tikhomirov}, -} - -@article {MR1959581, - AUTHOR = {Donaldson, Simon K.}, - TITLE = {Holomorphic discs and the complex {M}onge-{A}mpère equation}, - JOURNAL = {J. Symplectic Geom.}, - FJOURNAL = {The Journal of Symplectic Geometry}, - VOLUME = {1}, - YEAR = {2002}, - NUMBER = {2}, - PAGES = {171--196}, - ISSN = {1527-5256}, - MRCLASS = {32W20 (32Q15 58J32)}, - MRNUMBER = {1959581}, -MRREVIEWER = {David F. 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Steklova. - Rossi\u{i}skaya Akademiya Nauk}, - VOLUME = 240, - YEAR = 2003, - NUMBER = {Biratsion. Geom. Line\u{i}n. Sist. Konechno Porozhdennye - Algebry}, - PAGES = {82--219}, - ISSN = {0371-9685}, - MRCLASS = {14E30}, - MRNUMBER = 1993750, - MRREVIEWER = {Sándor J. Kovács}, -} - -@article {MR2036231, - AUTHOR = {Chen, Jungkai A. and Hacon, Christopher D.}, - TITLE = {On the irregularity of the image of the {I}itaka fibration}, - JOURNAL = {Comm. Algebra}, - FJOURNAL = {Communications in Algebra}, - VOLUME = {32}, - YEAR = {2004}, - NUMBER = {1}, - PAGES = {203--215}, - ISSN = {0092-7872}, - MRCLASS = {14C20 (14D06)}, - MRNUMBER = {2036231}, -MRREVIEWER = {Miguel A. Barja}, - DOI = {10.1081/AGB-120027861}, - URL = {https://doi.org/10.1081/AGB-120027861}, -} - -@article {MR2041755, - AUTHOR = {Yamanoi, Katsutoshi}, - TITLE = {Algebro-geometric version of {N}evanlinna's lemma on logarithmic derivative and applications}, - JOURNAL = {Nagoya Math. J.}, - FJOURNAL = {Nagoya Mathematical Journal}, - NOTE = {\href{https://doi.org/10.1017/S0027763000008710}{DOI:10.1017/S0027763000008710}}, - VOLUME = {173}, - YEAR = {2004}, - PAGES = {23--63}, - ISSN = {0027-7630}, - MRCLASS = {32H30}, - MRNUMBER = {2041755}, -MRREVIEWER = {William A. Cherry}, - DOI = {10.1017/S0027763000008710}, - URL = {https://doi.org/10.1017/S0027763000008710}, -} - -@article{MR2057020, - Author = {Keel, Sean and Matsuki, Kenji and {\hbox{Mc}}Kernan, James}, - Coden = {DUMJAO}, - Fjournal = {Duke Mathematical Journal}, - Issn = {0012-7094}, - Journal = {Duke Math. 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J.}, - FJOURNAL = {Moscow Mathematical Journal}, - VOLUME = 4, - YEAR = 2004, - NOTE = {Available at - \url{https://www.ams.org/distribution/mmj/vol4-4-2004/cont4-4-2004.html}}, - NUMBER = 4, - PAGES = {847--868, 981}, - ISSN = {1609-3321}, - MRCLASS = {32C38 (18E30)}, - MRNUMBER = 2124169, - MRREVIEWER = {Luisa Fiorot}, -} - -@article {MR2134273, - AUTHOR = {Ambro, Florin}, - TITLE = {The moduli {$b$}-divisor of an lc-trivial fibration}, - JOURNAL = {Compos. Math.}, - FJOURNAL = {Compositio Mathematica}, - VOLUME = {141}, - YEAR = {2005}, - NOTE = {\href{https://doi.org/10.1112/S0010437X04001071}{DOI:10.1112/S0010437X04001071}. Preprint \href{https://arxiv.org/abs/math/0308143}{arXiv:math/0308143}}, - NUMBER = {2}, - PAGES = {385--403}, - ISSN = {0010-437X}, - MRCLASS = {14E30 (14N30)}, - MRNUMBER = {2134273}, -MRREVIEWER = {Mark Gross}, - DOI = {10.1112/S0010437X04001071}, - URL = {https://doi.org/10.1112/S0010437X04001071}, -} - -@article {MR2141325, - AUTHOR = {Prokhorov, Yuri G.}, - TITLE = {The degree of {F}ano threefolds with canonical {G}orenstein singularities}, - JOURNAL = {Mat. Sb.}, - FJOURNAL = {Matematicheski\u{\i} Sbornik}, - VOLUME = {196}, - YEAR = {2005}, - NOTE = {\href{https://doi.org/10.1070/SM2005v196n01ABEH000873}{DOI:10.1070/SM2005v196n01ABEH000873}}, - NUMBER = {1}, - PAGES = {81--122}, - ISSN = {0368-8666}, - MRCLASS = {14J45 (14E15)}, - MRNUMBER = {2141325}, -MRREVIEWER = {Jaros\l aw A. 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Ltd., Hackensack, NJ}, - YEAR = 2005, - PAGES = {xii+148}, - ISBN = {981-256-496-9}, - MRCLASS = {32F45 (32H02 32H04 32Q45)}, - MRNUMBER = 2194466, - MRREVIEWER = {William A. Cherry}, - DOI = {10.1142/5936}, - URL = {https://doi.org/10.1142/5936}, -} - -@article {MR2196000, - AUTHOR = {Flenner, Hubert and Zaidenberg, Mikhail}, - TITLE = {Locally nilpotent derivations on affine surfaces with a {$\Bbb C^*$}-action}, - JOURNAL = {Osaka J. Math.}, - FJOURNAL = {Osaka Journal of Mathematics}, - VOLUME = 42, - YEAR = 2005, - NOTE = {\href{http://projecteuclid.org/euclid.ojm/1153494558}{euclid.ojm/1153494558}}, - NUMBER = 4, - PAGES = {931--974}, - ISSN = {0030-6126}, - MRCLASS = {14R20 (14R05)}, - MRNUMBER = 2196000, - MRREVIEWER = {Adrien Dubouloz}, - URL = {http://projecteuclid.org/euclid.ojm/1153494558}, -} - -@incollection{MR2210794, - Author = {Drézet, Jean-Marc}, - Booktitle = {Algebraic group actions and quotients}, - Mrclass = {14L30 (14L24)}, - Mrnumber = {2210794 (2006k:14082)}, - Mrreviewer = {Lucy Moser-Jauslin}, - Pages = {39--89}, - Publisher = {Hindawi Publ. Corp., Cairo}, - Title = {Luna's slice theorem and applications}, - Year = 2004 -} - -@article {MR2221132, - AUTHOR = {Kaledin, Dmitry and Lehn, Manfred and Sorger, Christoph}, - TITLE = {Singular symplectic moduli spaces}, - JOURNAL = {Invent. Math.}, - FJOURNAL = {Inventiones Mathematicae}, - VOLUME = 164, - YEAR = 2006, - NOTE = {\href{https://doi.org/10.1007/s00222-005-0484-6}{DOI:10.1007/s00222-005-0484-6}.}, - NUMBER = 3, - PAGES = {591--614}, - ISSN = {0020-9910}, - MRCLASS = {14D20 (14J28 14J60)}, - MRNUMBER = 2221132, - MRREVIEWER = {Carlo Giovanni Madonna}, - DOI = {10.1007/s00222-005-0484-6}, - URL = {https://doi.org/10.1007/s00222-005-0484-6}, -} - -@article{MR2229475, - Author = {Peternell, Thomas}, - Doi = {10.1142/S0129167X0600362X}, - Fjournal = {International Journal of Mathematics}, - Issn = {0129-167X}, - Journal = {Internat. J. Math.}, - Mrclass = {14E30 (14J40)}, - Mrnumber = {2229475 (2007b:14034)}, - Mrreviewer = {James McKernan}, - Number = 5, - Pages = {619--631}, - Title = {Kodaira dimension of subvarieties. {II}}, - Url = {https://doi.org/10.1142/S0129167X0600362X}, - Volume = 17, - Year = 2006, - Bdsk-Url-1 = {https://doi.org/10.1142/S0129167X0600362X} -} - -@article {MR2231055, - AUTHOR = {Bruzzo, Ugo and Hernández Ruipérez, Daniel}, - TITLE = {Semistability vs.\ nefness for ({H}iggs) vector bundles}, - JOURNAL = {Differential Geom. Appl.}, - FJOURNAL = {Differential Geometry and its Applications}, - VOLUME = 24, - YEAR = 2006, - Note = - {\href{https://doi.org/10.1016/j.difgeo.2005.12.007}{DOI:10.1016/j.difgeo.2005.12.007}}, - NUMBER = 4, - PAGES = {403--416}, - ISSN = {0926-2245}, - CODEN = {DGAPEO}, - MRCLASS = {14H60 (14J60)}, - MRNUMBER = 2231055, - MRREVIEWER = {Adrian Langer}, - DOI = {10.1016/j.difgeo.2005.12.007}, - URL = {https://doi.org/10.1016/j.difgeo.2005.12.007}, -} - -@article{MR2239523, - Author = {Keum, Jong-Hae}, - Coden = {TPLGAF}, - Doi = {10.1016/j.top.2006.06.006}, - Fjournal = {Topology. An International Journal of Mathematics}, - Issn = {0040-9383}, - Journal = {Topology}, - Mrclass = {14J29 (14J27)}, - Mrnumber = {2239523 (2008b:14065)}, - Number = 5, - Pages = {919--927}, - Title = {A fake projective plane with an order 7 automorphism}, - Note = - {\href{https://doi.org/10.1016/j.top.2006.06.006}{DOI:10.1016/j.top.2006.06.006}}, - Url = {https://doi.org/10.1016/j.top.2006.06.006}, - Volume = 45, - Year = 2006, - Bdsk-Url-1 = {https://doi.org/10.1016/j.top.2006.06.006} -} - -@book {MR2243012, - AUTHOR = {Ballmann, Werner}, - TITLE = {Lectures on {K}ähler manifolds}, - SERIES = {ESI Lectures in Mathematics and Physics}, - PUBLISHER = {European Mathematical Society (EMS), Zürich}, - YEAR = 2006, - PAGES = {x+172}, - ISBN = {978-3-03719-025-8; 3-03719-025-6}, - MRCLASS = {32Q15 (53C55)}, - MRNUMBER = {2243012 (2007e:32026)}, - MRREVIEWER = {Joel Fine}, - DOI = {10.4171/025}, - URL = {https://doi.org/10.4171/025}, -} - -@book{MR2247485, - Address = {Berlin}, - Author = {Jost, Jürgen}, - Doi = {10.1007/978-3-540-33067-7}, - Edition = {Third}, - Isbn = {978-3-540-33065-3; 3-540-33065-8}, - Mrclass = {32G15 (58E20)}, - Mrnumber = {2247485 (2007b:32024)}, - Note = {An introduction to contemporary mathematics}, - Pages = {xviii+277}, - Publisher = {Springer-Verlag}, - Series = {Universitext}, - Title = {Compact {R}iemann surfaces}, - Url = {https://doi.org/10.1007/978-3-540-33067-7}, - Year = 2006, - Bdsk-Url-1 = {https://doi.org/10.1007/978-3-540-33067-7} -} - -@article {MR2281877, - AUTHOR = {Mochizuki, Takuro}, - TITLE = {Asymptotic behaviour of tame harmonic bundles and an - application to pure twistor {$D$}-modules. {I}}, - JOURNAL = {Mem. Amer. Math. Soc.}, - FJOURNAL = {Memoirs of the American Mathematical Society}, - VOLUME = 185, - YEAR = 2007, - NOTE = - {\href{https://doi.org/10.1090/memo/0869}{DOI:10.1090/memo/0869}}, - NUMBER = 869, - PAGES = {xii+324}, - ISSN = {0065-9266}, - MRCLASS = {32S40 (14C30 53C07 53C43)}, - MRNUMBER = 2281877, - MRREVIEWER = {Carlos T. Simpson}, - DOI = - {\href{https://doi.org/10.1090/memo/0869}{DOI:10.1090/memo/0869}}, - URL = {https://doi.org/10.1090/memo/0869}, -} - -@article {MR2283665, - AUTHOR = {Mochizuki, Takuro}, - TITLE = {Asymptotic behaviour of tame harmonic bundles and an - application to pure twistor {$D$}-modules. {II}}, - JOURNAL = {Mem. Amer. Math. Soc.}, - FJOURNAL = {Memoirs of the American Mathematical Society}, - VOLUME = 185, - YEAR = 2007, - NOTE = - {\href{https://doi.org/10.1090/memo/0870}{DOI:10.1090/memo/0870}}, - NUMBER = 870, - PAGES = {xii+565}, - ISSN = {0065-9266}, - CODEN = {MAMCAU}, - MRCLASS = {32S40 (14C30 53C07 53C43)}, - MRNUMBER = 2283665, - MRREVIEWER = {Carlos T. Simpson}, - DOI = {10.1090/memo/0870}, - URL = {https://doi.org/10.1090/memo/0870}, -} - -@book{MR2290112, - Address = {Berlin}, - Author = {Greuel, G.-M. and Lossen, C. and Shustin, E.}, - Isbn = {978-3-540-28380-5; 3-540-28380-3}, - Mrclass = {32Sxx (14B05)}, - Mrnumber = {2290112 (2008b:32013)}, - Mrreviewer = {Vasile Brînz{ă}nescu}, - Pages = {xii+471}, - Publisher = {Springer}, - Series = {Springer Monographs in Mathematics}, - Title = {Introduction to singularities and deformations}, - Year = 2007 -} - -@article {MR2310103, - AUTHOR = {Mochizuki, Takuro}, - TITLE = {Kobayashi-{H}itchin correspondence for tame harmonic bundles - and an application}, - JOURNAL = {Astérisque}, - FJOURNAL = {Astérisque}, - NUMBER = 309, - YEAR = 2006, - PAGES = {viii+117}, - ISSN = {0303-1179}, - ISBN = {978-2-85629-226-6}, - MRCLASS = {32Q20 (14D07 14J60 32G20 53C07)}, - MRNUMBER = 2310103, - MRREVIEWER = {Julien Keller}, -} - -@article{MR2332355, - Author = {Hwang, Jun-Muk}, - Coden = {ASENAH}, - Doi = {10.1016/j.ansens.2006.12.001}, - Fjournal = {Annales Scientifiques de l'École Normale Supérieure. Quatrième - Série}, - Issn = {0012-9593}, - Journal = {Ann. Sci. École Norm. Sup. (4)}, - Mrclass = {32G99 (14D15 32J27)}, - Mrnumber = {2332355 (2008m:32028)}, - Mrreviewer = {Stefan Kebekus}, - Number = 1, - Pages = {179--189}, - Title = {Deformation of holomorphic maps onto the blow-up of the - projective plane}, - Url = {https://doi.org/10.1016/j.ansens.2006.12.001}, - Volume = 40, - Year = 2007, - Bdsk-Url-1 = {https://doi.org/10.1016/j.ansens.2006.12.001} -} - -@article{MR2336831, - Author = {Hwang, Jun-Muk}, - Coden = {AIFUA7}, - Fjournal = {Université de Grenoble. Annales de l'Institut Fourier}, - Issn = {0373-0956}, - Journal = {Ann. Inst. Fourier (Grenoble)}, - Mrclass = {14J45 (32H02)}, - Mrnumber = {2336831 (2008g:14064)}, - Mrreviewer = {Andreas Höring}, - Number = 3, - Pages = {815--823}, - Title = {Deformation of holomorphic maps onto {F}ano manifolds of - second and fourth {B}etti numbers 1}, - Url = {http://aif.cedram.org/item?id=AIF_2007__57_3_815_0}, - Volume = 57, - Year = 2007, - Bdsk-Url-1 = {http://aif.cedram.org/item?id=AIF_2007__57_3_815_0} -} - -@article {MR2343296, - AUTHOR = {Bradlow, Steven B. and García-Prada, Oscar and Gothen, - Peter B.}, - TITLE = {What is{$\dots$} a {H}iggs bundle?}, - JOURNAL = {Notices Amer. Math. Soc.}, - FJOURNAL = {Notices of the American Mathematical Society}, - VOLUME = 54, - YEAR = 2007, - NUMBER = 8, - PAGES = {980--981}, - ISSN = {0002-9920}, - MRCLASS = {53C07 (14D21)}, - MRNUMBER = {2343296 (2008e:53035)}, - MRREVIEWER = {Graeme Wilkin}, -} - -@article{MR2344354, - Author = {Catanese, Fabrizio}, - Coden = {JDGEAS}, - Fjournal = {Journal of Differential Geometry}, - Issn = {0022-040X}, - Journal = {J. Differential Geom.}, - Mrclass = {14E99 (32G05 32J15)}, - Mrnumber = {2344354 (2008k:14038)}, - Mrreviewer = {Vasile Brînz{ă}nescu}, - Note = {With an appendix by Sönke - Rollenske. \href{http://projecteuclid.org/euclid.jdg/1185550815}{euclid.jdg/1185550815}}, - Number = 1, - Pages = {43--75}, - Title = {Q.{E}.{D}. for algebraic varieties}, - Url = {http://projecteuclid.org/euclid.jdg/1185550815}, - Volume = 77, - Year = 2007, - Bdsk-Url-1 = {http://projecteuclid.org/euclid.jdg/1185550815} -} - -@book{MR2352762, - Address = {Oxford}, - Author = {{Corti et al.}, Alessio}, - Isbn = {978-0-19-857061-5}, - Mrclass = {14E30 (14-06)}, - Mrnumber = {2352762 (2008j:14031)}, - Mrreviewer = {Michael A. van Opstall}, - Pages = {x+189}, - Publisher = {Oxford University Press}, - Series = {Oxford Lecture Series in Mathematics and its Applications}, - Title = {Flips for 3-folds and 4-folds}, - Volume = 35, - Year = 2007 -} - -@incollection {MR2359346, - AUTHOR = {Kollár, János}, - TITLE = {Kodaira's canonical bundle formula and adjunction}, - BOOKTITLE = {Flips for 3-folds and 4-folds}, - SERIES = {Oxford Lecture Ser. Math. Appl.}, - VOLUME = {35}, - PAGES = {134--162}, - PUBLISHER = {Oxford Univ. Press, Oxford}, - YEAR = {2007}, - NOTE = {\href{https://doi.org/10.1093/acprof:oso/9780198570615.003.0008}{DOI:10.1093/acprof:oso/9780198570615.003.0008}}, - MRCLASS = {14E30 (14N30)}, - MRNUMBER = {2359346}, - DOI = {10.1093/acprof:oso/9780198570615.003.0008}, - URL = {https://doi.org/10.1093/acprof:oso/9780198570615.003.0008}, -} - -@book{MR2359489, - Author = {Wells, Jr., Raymond O.}, - Doi = {10.1007/978-0-387-73892-5}, - Edition = {Third}, - Isbn = {978-0-387-73891-8}, - Mrclass = {32-01 (58-01)}, - Mrnumber = {2359489 (2008g:32001)}, - Note = {With a new appendix by Oscar Garcia-Prada}, - Pages = {xiv+299}, - Publisher = {Springer, New York}, - Series = {Graduate Texts in Mathematics}, - Title = {Differential analysis on complex manifolds}, - Url = {https://doi.org/10.1007/978-0-387-73892-5}, - Volume = 65, - Year = 2008, - Bdsk-Url-1 = {https://doi.org/10.1007/978-0-387-73892-5} -} - -@article {MR2364074, - AUTHOR = {Bruzzo, Ugo and Gra{\~n}a Otero, Beatriz}, - TITLE = {Metrics on semistable and numerically effective {H}iggs - bundles}, - JOURNAL = {J. Reine Angew. Math.}, - FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's - Journal]}, - VOLUME = 612, - YEAR = 2007, - PAGES = {59--79}, - ISSN = {0075-4102}, - CODEN = {JRMAA8}, - MRCLASS = {32L05 (32Q20)}, - MRNUMBER = 2364074, - MRREVIEWER = {Graeme Wilkin}, - DOI = {10.1515/CRELLE.2007.084}, - URL = {https://doi.org/10.1515/CRELLE.2007.084}, -} - -@article {MR2369185, - AUTHOR = {Biswas, Indranil and Gómez, Tomás L.}, - TITLE = {Connections and {H}iggs fields on a principal bundle}, - JOURNAL = {Ann. Global Anal. Geom.}, - FJOURNAL = {Annals of Global Analysis and Geometry}, - VOLUME = {33}, - YEAR = {2008}, - NOTE = {\href{https://doi.org/10.1007/s10455-007-9072-x}{DOI:10.1007/s10455-007-9072-x}}, - NUMBER = {1}, - PAGES = {19--46}, - ISSN = {0232-704X}, - MRCLASS = {32L05 (14L10 53C07)}, - MRNUMBER = {2369185}, -MRREVIEWER = {Graeme Wilkin}, - DOI = {10.1007/s10455-007-9072-x}, - URL = {https://doi.org/10.1007/s10455-007-9072-x}, -} - -@article {MR2372739, - AUTHOR = {Wittenberg, Olivier}, - TITLE = {On {A}lbanese torsors and the elementary obstruction}, - JOURNAL = {Math. Ann.}, - FJOURNAL = {Mathematische Annalen}, - VOLUME = {340}, - YEAR = {2008}, - NOTE = {\href{https://doi.org/10.1007/s00208-007-0170-7}{DOI:10.1007/s00208-007-0170-7}. Preprint \href{https://arXiv.org/abs/math/0611284}{arXiv:math/0611284}}, - NUMBER = {4}, - PAGES = {805--838}, - ISSN = {0025-5831}, - MRCLASS = {14C25 (14K05)}, - MRNUMBER = {2372739}, -MRREVIEWER = {Francisco J. Plaza Mart\'{\i}n}, - DOI = {10.1007/s00208-007-0170-7}, - URL = {https://doi.org/10.1007/s00208-007-0170-7}, -} - -@book {MR2377148, - AUTHOR = {Bryant, John and Sangwin, Chris}, - TITLE = {How round is your circle? Where engineering and mathematics meet.}, - NOTE = {\href{https://doi.org/10.1515/9781400837953.303}{DOI:10.1515/9781400837953.303}}, - PUBLISHER = {Princeton University Press, Princeton, NJ}, - YEAR = {2008}, - PAGES = {xxii+306}, - ISBN = {978-0-691-13118-4}, - MRCLASS = {00A06 (00A05 51M15 51M99 70-01 70Bxx)}, - MRNUMBER = {2377148}, -MRREVIEWER = {Andrew Edward Whelan}, -} - -@article{MR2383493, - Author = {Abe, Takuro and Yoshinaga, Masahiko}, - Coden = {PAMYAR}, - Doi = {10.1090/S0002-9939-08-09367-2}, - Fjournal = {Proceedings of the American Mathematical Society}, - Issn = {0002-9939}, - Journal = {Proc. Amer. Math. Soc.}, - Mrclass = {14F05 (14J60)}, - Mrnumber = {2383493 (2009f:14029)}, - Mrreviewer = {Vasile Brînz{ă}nescu}, - Number = 6, - Pages = {1887--1891}, - Title = {Splitting criterion for reflexive sheaves}, - Url = {https://doi.org/10.1090/S0002-9939-08-09367-2}, - Volume = 136, - Year = 2008, - Bdsk-Url-1 = {https://doi.org/10.1090/S0002-9939-08-09367-2} -} - -@article{MR2399162, - Author = {Rollenske, Sönke}, - Coden = {MAANA}, - Doi = {10.1007/s00208-007-0206-z}, - Fjournal = {Mathematische Annalen}, - Issn = {0025-5831}, - Journal = {Math. Ann.}, - Mrclass = {53C56 (55T99 58A14)}, - Mrnumber = {2399162 (2009c:53099)}, - Mrreviewer = {Sergio Console}, - Number = 3, - Pages = {623--628}, - Title = {The {F}rölicher spectral sequence can be arbitrarily non-degenerate}, - Url = {https://doi.org/10.1007/s00208-007-0206-z}, - Volume = 341, - Year = 2008, - Bdsk-Url-1 = {https://doi.org/10.1007/s00208-007-0206-z} -} - -@article{MR2400877, - Author = {Kollár, János}, - Fjournal = {Pure and Applied Mathematics Quarterly}, - Issn = {1558-8599}, - Journal = {Pure Appl. Math. Q.}, - Mrclass = {14J80 (14J17 57N13)}, - Mrnumber = {2400877 (2009b:14086)}, - Mrreviewer = {Arnaud Beauville}, - Number = {2, part 1}, - Pages = {203--236}, - Title = {Is there a topological {B}ogomolov-{M}iyaoka-{Y}au inequality?}, - Volume = 4, - Year = 2008 -} - -@article{MR2429621, - Author = {Aprodu, Marian and Kebekus, Stefan and Peternell, Thomas}, - Coden = {MAZEAX}, - Doi = {10.1007/s00209-007-0282-5}, - Fjournal = {Mathematische Zeitschrift}, - Issn = {0025-5874}, - Journal = {Math. Z.}, - Mrclass = {14E20 (14J45)}, - Mrnumber = {2429621 (2009m:14017)}, - Mrreviewer = {Jarosław A. Wiśniewski}, - Number = 2, - Pages = {431--449}, - Title = {Galois coverings and endomorphisms of projective varieties}, - Url = {https://doi.org/10.1007/s00209-007-0282-5}, - Volume = 260, - Year = 2008, - Bdsk-Url-1 = {https://doi.org/10.1007/s00209-007-0282-5} -} - -@article {MR2439607, - AUTHOR = {Araujo, Carolina and Druel, Stéphane and Kovács, Sándor J.}, - TITLE = {Cohomological characterizations of projective spaces and - hyperquadrics}, - JOURNAL = {Invent. Math.}, - FJOURNAL = {Inventiones Mathematicae}, - VOLUME = 174, - YEAR = 2008, - NUMBER = 2, - Note = {\href{https://doi.org/10.1007/s00222-008-0130-1}{DOI:10.1007/s00222-008-0130-1}}, - PAGES = {233--253}, - ISSN = {0020-9910}, - CODEN = {INVMBH}, - MRCLASS = {14E30 (14F10 14M20)}, - MRNUMBER = 2439607, - MRREVIEWER = {Andreas Höring}, - DOI = {10.1007/s00222-008-0130-1}, - URL = {https://doi.org/10.1007/s00222-008-0130-1}, -} - -@article{MR2443971, - Author = {Keum, Jong-Hae}, - Doi = {10.2140/gt.2008.12.2497}, - Fjournal = {Geometry \& Topology}, - Issn = {1465-3060}, - Journal = {Geom. Topol.}, - Mrclass = {14J29 (14E15)}, - Mrnumber = {2443971 (2009g:14042)}, - Mrreviewer = {Marco Andreatta}, - Number = 4, - Pages = {2497--2515}, - Title = {Quotients of fake projective planes}, - Note = {\href{https://doi.org/10.2140/gt.2008.12.2497}{DOI: - 10.2140/gt.2008.12.2497}}, - Url = {https://doi.org/10.2140/gt.2008.12.2497}, - Volume = 12, - Year = 2008, - Bdsk-Url-1 = {https://doi.org/10.2140/gt.2008.12.2497} -} - -@article {MR2448282, - AUTHOR = {Prokhorov, Yuri G. and Shokurov, Vyacheslav V.}, - TITLE = {Towards the second main theorem on complements}, - JOURNAL = {J. Algebraic Geom.}, - FJOURNAL = {Journal of Algebraic Geometry}, - VOLUME = 18, - YEAR = 2009, - NUMBER = 1, - NOTE = {\href{https://doi.org/10.1090/S1056-3911-08-00498-0}{DOI:10.1090/S1056-3911-08-00498-0}}, - PAGES = {151--199}, - ISSN = {1056-3911}, - MRCLASS = {14C20 (14J45)}, - MRNUMBER = 2448282, - MRREVIEWER = {Alexandr V. Pukhlikov}, - DOI = {10.1090/S1056-3911-08-00498-0}, - URL = {https://doi.org/10.1090/S1056-3911-08-00498-0}, -} - -@article{MR2449950, - Author = {Berndtsson, Bo and Păun, Mihai}, - Coden = {DUMJAO}, - Doi = {10.1215/00127094-2008-054}, - Fjournal = {Duke Mathematical Journal}, - Issn = {0012-7094}, - Journal = {Duke Math. J.}, - Mrclass = {32L15 (14J40)}, - Mrnumber = {2449950 (2009k:32020)}, - Mrreviewer = {James McKernan}, - Number = 2, - Pages = {341--378}, - Title = {Bergman kernels and the pseudoeffectivity of relative - canonical bundles}, - Note = {\href{https://doi.org/10.1215/00127094-2008-054}{DOI: - 10.1215/00127094-2008-054}}, - Url = {https://doi.org/10.1215/00127094-2008-054}, - Volume = 145, - Year = 2008, - Bdsk-Url-1 = {https://doi.org/10.1215/00127094-2008-054} -} - -@incollection{MR2483953, - Address = {Providence, RI}, - Author = {Kovács, Sándor J.}, - Booktitle = {Algebraic geometry---{S}eattle 2005. {P}art 2}, - Mrclass = {14J10 (14-02 14D20 14E30)}, - Mrnumber = {2483953 (2009m:14051)}, - Mrreviewer = {James McKernan}, - Pages = {711--743}, - Publisher = {Amer. Math. Soc.}, - Series = {Proc. Sympos. Pure Math.}, - Title = {Young person's guide to moduli of higher dimensional - varieties}, - Volume = 80, - Year = 2009 -} - -@article{MR2497488, - Author = {Zhang, Yuguang}, - Coden = {PAMYAR}, - Doi = {10.1090/S0002-9939-09-09838-4}, - Fjournal = {Proceedings of the American Mathematical Society}, - Issn = {0002-9939}, - Journal = {Proc. Amer. Math. Soc.}, - Mrclass = {32Q20 (32L05 53C25 53C44)}, - Mrnumber = {2497488 (2010b:32036)}, - Mrreviewer = {Julien Keller}, - Number = 8, - Pages = {2749--2754}, - Title = {Miyaoka-{Y}au inequality for minimal projective manifolds of - general type}, - Note = {\href{https://doi.org/10.1090/S0002-9939-09-09838-4}{DOI: - 10.1090/S0002-9939-09-09838-4}}, - Url = {https://doi.org/10.1090/S0002-9939-09-09838-4}, - Volume = 137, - Year = 2009, - Bdsk-Url-1 = {https://doi.org/10.1090/S0002-9939-09-09838-4} -} - -@inproceedings{MR2500573, - Author = {Włodarczyk, Jarosław}, - Booktitle = {Proceedings of {G}ökova {G}eometry-{T}opology {C}onference - 2008}, - Mrclass = {32S45 (32C25)}, - Mrnumber = {2500573 (2011e:32039)}, - Pages = {31--63}, - Publisher = {Gökova Geometry/Topology Conference (GGT), Gökova}, - Title = {Resolution of singularities of analytic spaces}, - Year = 2009 -} - -@article {MR2505296, - AUTHOR = {Eyssidieux, Philippe and Guedj, Vincent and Zeriahi, Ahmed}, - TITLE = {Singular {K}ähler-{E}instein metrics}, - JOURNAL = {J. Amer. Math. Soc.}, - FJOURNAL = {Journal of the American Mathematical Society}, - VOLUME = 22, - YEAR = 2009, - NUMBER = 3, - PAGES = {607--639}, - ISSN = {0894-0347}, - MRCLASS = {32Q20 (31C10 32J27 32Q25 32W20)}, - MRNUMBER = {2505296 (2010k:32031)}, - MRREVIEWER = {Zhou Zhang}, - NOTE = {\href{https://doi.org/10.1090/S0894-0347-09-00629-8}{DOI:10.1090/S0894-0347-09-00629-8}}, - DOI = {10.1090/S0894-0347-09-00629-8}, - URL = {https://doi.org/10.1090/S0894-0347-09-00629-8}, -} - -@book{MR2514037, - Author = {Mumford, David}, - Isbn = {978-81-85931-86-9; 81-85931-86-0}, - Mrclass = {14Kxx}, - Mrnumber = {2514037 (2010e:14040)}, - Note = {With appendices by C. P. Ramanujam and Yuri Manin, Corrected - reprint of the second (1974) edition}, - Pages = {xii+263}, - Publisher = {Published for the Tata Institute of Fundamental Research, - Bombay}, - Series = {Tata Institute of Fundamental Research Studies in Mathematics}, - Title = {Abelian varieties}, - Volume = 5, - Year = 2008 -} - -@book {MR2522486, - AUTHOR = {Goodman, Roe and Wallach, Nolan R.}, - TITLE = {Symmetry, representations, and invariants}, - SERIES = {Graduate Texts in Mathematics}, - VOLUME = 255, - PUBLISHER = {Springer, Dordrecht}, - YEAR = 2009, - PAGES = {xx+716}, - ISBN = {978-0-387-79851-6}, - MRCLASS = {20G05 (14L35 17B10 20C30 20G20 22E46)}, - MRNUMBER = 2522486, - MRREVIEWER = {Vladimir V. Shchigolev}, - NOTE = - {\href{https://doi.org/10.1007/978-0-387-79852-3}{DOI:10.1007/978-0-387-79852-3}.}, - DOI = {10.1007/978-0-387-79852-3}, - URL = {https://doi.org/10.1007/978-0-387-79852-3}, -} - -@article {MR2538503, - AUTHOR = {Tosatti, Valentino}, - TITLE = {Limits of {C}alabi-{Y}au metrics when the {K}ähler class - degenerates}, - JOURNAL = {J. Eur. Math. Soc. (JEMS)}, - FJOURNAL = {Journal of the European Mathematical Society (JEMS)}, - VOLUME = 11, - YEAR = 2009, - NUMBER = 4, - NOTE = - {\href{https://doi.org/10.4171/JEMS/165}{DOI:b10.4171/JEMS/165}. Preprint - \href{http://arxiv.org/abs/0710.4579}{arXiv:0710.4579}}, - PAGES = {755--776}, - ISSN = {1435-9855}, - MRCLASS = {32Q25 (32Q20 32W20)}, - MRNUMBER = {2538503 (2010j:32039)}, - MRREVIEWER = {Julien Keller}, - DOI = {10.4171/JEMS/165}, - URL = {https://doi.org/10.4171/JEMS/165}, -} - -@book {MR2542964, - AUTHOR = {Lehrer, Gustav I. and Taylor, Donald E.}, - TITLE = {Unitary reflection groups}, - SERIES = {Australian Mathematical Society Lecture Series}, - VOLUME = {20}, - PUBLISHER = {Cambridge University Press, Cambridge}, - YEAR = {2009}, - PAGES = {viii+294}, - ISBN = {978-0-521-74989-3}, - MRCLASS = {20F55}, - MRNUMBER = {2542964}, -MRREVIEWER = {O. V. Shvartsman}, -} - -@article {MR2545454, - AUTHOR = {Biswas, Indranil}, - TITLE = {Semistability and restrictions of tangent bundle to curves}, - JOURNAL = {Geom. Dedicata}, - FJOURNAL = {Geometriae Dedicata}, - VOLUME = {142}, - YEAR = {2009}, - PAGES = {37--46}, - ISSN = {0046-5755}, - MRCLASS = {14F05 (32L10)}, - MRNUMBER = {2545454}, -MRREVIEWER = {Graeme Wilkin}, - NOTE = {\href{https://doi.org/10.1007/s10711-009-9356-3}{DOI:10.1007/s10711-009-9356-3}. Preprint \href{https://arxiv.org/abs/0901.4161}{arXiv:0901.4161}}, - DOI = {10.1007/s10711-009-9356-3}, - URL = {https://doi.org/10.1007/s10711-009-9356-3}, -} - -@article {MR2567402, - AUTHOR = {Serre, Jean-Pierre}, - TITLE = {A {M}inkowski-style bound for the orders of the finite - subgroups of the {C}remona group of rank 2 over an arbitrary - field}, - JOURNAL = {Mosc. Math. J.}, - FJOURNAL = {Moscow Mathematical Journal}, - VOLUME = 9, - YEAR = 2009, - NUMBER = 1, - PAGES = {193--208, back matter}, - ISSN = {1609-3321}, - MRCLASS = {14E07 (14J26)}, - MRNUMBER = 2567402, - MRREVIEWER = {Alberto Calabri}, -} - -@book{MR2583634, - Address = {New York}, - Author = {Hartshorne, Robin}, - Doi = {10.1007/978-1-4419-1596-2}, - Isbn = {978-1-4419-1595-5}, - Mrclass = {14D15 (13D10 14B07 14B12)}, - Mrnumber = {2583634 (2011c:14023)}, - Mrreviewer = {Arvid Siqveland}, - Pages = {viii+234}, - Publisher = {Springer}, - Series = {Graduate Texts in Mathematics}, - Title = {Deformation theory}, - Url = {https://doi.org/10.1007/978-1-4419-1596-2}, - Volume = 257, - Year = 2010, - Bdsk-Url-1 = {https://doi.org/10.1007/978-1-4419-1596-2} -} - -@article {MR2586735, - AUTHOR = {Cartwright, Donald I. and Steger, Tim}, - TITLE = {Enumeration of the 50 fake projective planes}, - JOURNAL = {C. R. Math. Acad. Sci. Paris}, - FJOURNAL = {Comptes Rendus Mathématique. Académie des Sciences. Paris}, - VOLUME = 348, - YEAR = 2010, - Note = - {\href{https://doi.org/10.1016/j.crma.2009.11.016}{DOI:10.1016/j.crma.2009.11.016}}, - NUMBER = {1-2}, - PAGES = {11--13}, - ISSN = {1631-073X}, - MRCLASS = {20G20 (14J99)}, - MRNUMBER = 2586735, - DOI = {10.1016/j.crma.2009.11.016}, - URL = {https://doi.org/10.1016/j.crma.2009.11.016}, -} - -@article{MR2587100, - Author = {Nakayama, Noboru and Zhang, De-Qi}, - Coden = {MAANA}, - Doi = {10.1007/s00208-009-0420-y}, - Fjournal = {Mathematische Annalen}, - Issn = {0025-5831}, - Journal = {Math. Ann.}, - Mrclass = {14J10 (14H20 32H50)}, - Mrnumber = {2587100 (2011c:14103)}, - Mrreviewer = {Karl Schwede}, - Number = 4, - Pages = {991--1018}, - Title = {Polarized endomorphisms of complex normal varieties}, - Url = {https://doi.org/10.1007/s00208-009-0420-y}, - Volume = 346, - Year = 2010, - Bdsk-Url-1 = {https://doi.org/10.1007/s00208-009-0420-y} -} - -@article{MR2587409, - Author = {Birkar, Caucher}, - Doi = {10.2140/ant.2009.3.951}, - Fjournal = {Algebra \& Number Theory}, - Issn = {1937-0652}, - Journal = {Algebra Number Theory}, - Mrclass = {14E30}, - Mrnumber = {2587409 (2011b:14034)}, - Mrreviewer = {Tomasz Szemberg}, - Number = 8, - Pages = {951--958}, - Title = {Log minimal models according to {S}hokurov}, - Url = {https://doi.org/10.2140/ant.2009.3.951}, - Volume = 3, - Year = 2009, - Bdsk-Url-1 = {https://doi.org/10.2140/ant.2009.3.951} -} - -@article {MR2592955, - AUTHOR = {Greb, Daniel}, - TITLE = {Projectivity of analytic {H}ilbert and {K}ähler quotients}, - JOURNAL = {Trans. Amer. Math. Soc.}, - FJOURNAL = {Transactions of the American Mathematical Society}, - VOLUME = 362, - YEAR = 2010, - NUMBER = 6, - PAGES = {3243--3271}, - ISSN = {0002-9947}, - CODEN = {TAMTAM}, - MRCLASS = {14L30 (14L24 32M05 53D20)}, - MRNUMBER = 2592955, - MRREVIEWER = {Dmitry A. Timash{\"e}v}, - DOI = {10.1090/S0002-9947-10-05000-2}, - URL = {https://doi.org/10.1090/S0002-9947-10-05000-2}, -} - -@article {MR2605324, - AUTHOR = {Gasbarri, Carlo}, - TITLE = {The strong {$abc$} conjecture over function fields (after {M}c{Q}uillan and {Y}amanoi)}, - NOTE = {Séminaire Bourbaki. Vol. 2007/2008. Preprint \href{https://arxiv.org/abs/0811.3153}{arXiv:0811.3153}}, - JOURNAL = {Astérisque}, - FJOURNAL = {Astérisque}, - NUMBER = 326, - YEAR = 2009, - PAGES = {Exp. No. 989, viii, 219--256 (2010)}, - ISSN = {0303-1179}, - ISBN = {978-285629-269-3}, - MRCLASS = {11D75 (11-02 11J97)}, - MRNUMBER = 2605324, - MRREVIEWER = {Robert Juricevic}, -} - -@article{MR2629988, - Author = {Kollár, János and Kovács, Sándor J.}, - Doi = {10.1090/S0894-0347-10-00663-6}, - Fjournal = {Journal of the American Mathematical Society}, - Issn = {0894-0347}, - Journal = {J. Amer. Math. Soc.}, - Mrclass = {14J17 (14B07 14E30)}, - Mrnumber = {2629988 (2011m:14061)}, - Mrreviewer = {Ali Sinan Sertöz}, - Note = {\href{https://doi.org/10.1090/S0894-0347-10-00663-6}{DOI:10.1090/S0894-0347-10-00663-6}}, - Number = 3, - Pages = {791--813}, - Title = {Log canonical singularities are {D}u {B}ois}, - Url = {https://doi.org/10.1090/S0894-0347-10-00663-6}, - Volume = 23, - Year = 2010, - Bdsk-Url-1 = {https://doi.org/10.1090/S0894-0347-10-00663-6} -} - -@article {MR2629989, - AUTHOR = {Kleiner, Bruce}, - TITLE = {A new proof of {G}romov's theorem on groups of polynomial - growth}, - JOURNAL = {J. Amer. Math. Soc.}, - FJOURNAL = {Journal of the American Mathematical Society}, - VOLUME = 23, - YEAR = 2010, - NOTE = - {\href{https://doi.org/10.1090/S0894-0347-09-00658-4}{DOI:10.1090/S0894-0347-09-00658-4}.}, - NUMBER = 3, - PAGES = {815--829}, - ISSN = {0894-0347}, - MRCLASS = {20F65 (20F67 20F69)}, - MRNUMBER = 2629989, - MRREVIEWER = {Fran{\c{c}}ois Dahmani}, - DOI = {10.1090/S0894-0347-09-00658-4}, - URL = {https://doi.org/10.1090/S0894-0347-09-00658-4}, -} - -@article {MR2648675, - AUTHOR = {Serre, Jean-Pierre}, - TITLE = {Le groupe de {C}remona et ses sous-groupes finis}, - NOTE = {Séminaire Bourbaki. Volume 2008/2009. Exposés 997--1011}, - JOURNAL = {Astéisque}, - FJOURNAL = {Astérisque}, - NUMBER = {332}, - YEAR = {2010}, - PAGES = {Exp. No. 1000, vii, 75--100}, - ISSN = {0303-1179}, - ISBN = {978-2-85629-291-4}, - MRCLASS = {14E07}, - MRNUMBER = {2648675}, -} - -@book{MR2665168, - Address = {Cambridge}, - Author = {Huybrechts, Daniel and Lehn, Manfred}, - Doi = {10.1017/CBO9780511711985}, - Edition = {Second}, - Isbn = {978-0-521-13420-0}, - Mrclass = {14D20 (14F05)}, - Mrnumber = {2665168 (2011e:14017)}, - Note = - {\href{https://doi.org/10.1017/CBO9780511711985}{DOI:10.1017/CBO9780511711985}}, - Pages = {xviii+325}, - Publisher = {Cambridge University Press}, - Series = {Cambridge Mathematical Library}, - Title = {The geometry of moduli spaces of sheaves}, - Url = {https://doi.org/10.1017/CBO9780511711985}, - Year = 2010, - Bdsk-Url-1 = {https://doi.org/10.1017/CBO9780511711985} -} - -@article {MR2667786, - AUTHOR = {Yamanoi, Katsutoshi}, - TITLE = {On fundamental groups of algebraic varieties and value distribution theory}, - JOURNAL = {Ann. Inst. Fourier (Grenoble)}, - FJOURNAL = {Université de Grenoble. Annales de l'Institut Fourier}, - VOLUME = {60}, - YEAR = {2010}, - NOTE = {\href{https://doi.org/10.5802/aif.2532}{DOI:10.5802/aif.2532}}, - NUMBER = {2}, - PAGES = {551--563}, - ISSN = {0373-0956}, - MRCLASS = {32H30 (14F35)}, - MRNUMBER = {2667786}, -MRREVIEWER = {William A. Cherry}, - URL = {http://aif.cedram.org/item?id=AIF_2010__60_2_551_0}, -} - -@article{MR2674856, - Author = {Höring, Andreas}, - Coden = {ENMAAR}, - Doi = {10.4171/LEM/56-1-4}, - Fjournal = {L'Enseignement Mathématique. Revue Internationale. 2e Série}, - Issn = {0013-8584}, - Journal = {Enseign. Math. (2)}, - Mrclass = {14D06 (14E30)}, - Mrnumber = {2674856 (2011g:14022)}, - Mrreviewer = {James McKernan}, - Number = {1-2}, - Pages = {87--142}, - Title = {Positivity of direct image sheaves---a geometric point of - view}, - Url = {https://doi.org/10.4171/LEM/56-1-4}, - Volume = 56, - Year = 2010, - Bdsk-Url-1 = {https://doi.org/10.4171/LEM/56-1-4} -} - -@book {MR2675155, - AUTHOR = {Görtz, Ulrich and Wedhorn, Torsten}, - TITLE = {Algebraic geometry {I}, Schemes, With Examples and Exercises}, - SERIES = {Advanced Lectures in Mathematics}, - PUBLISHER = {Vieweg + Teubner, Wiesbaden}, - YEAR = 2010, - PAGES = {viii+615}, - ISBN = {978-3-8348-0676-5}, - MRCLASS = {14-01}, - MRNUMBER = {2675155 (2011f:14001)}, - MRREVIEWER = {Cícero Carvalho}, - Note = - {\href{https://doi.org/10.1007/978-3-8348-9722-0}{DOI:10.1007/978-3-8348-9722-0}.}, - DOI = {10.1007/978-3-8348-9722-0}, - URL = {https://doi.org/10.1007/978-3-8348-9722-0}, -} - -@article {MR2739808, - AUTHOR = {Campana, Frédéric and Oguiso, Keiji and Peternell, Thomas}, - TITLE = {Non-algebraic hyperkähler manifolds}, - JOURNAL = {J. Differential Geom.}, - FJOURNAL = {Journal of Differential Geometry}, - VOLUME = {85}, - YEAR = {2010}, - NOTE = {\href{https://doi.org/10.4310/jdg/1292940689}{DOI:10.4310/jdg/1292940689}. Preprint \href{https://arxiv.org/abs/0804.1682}{arXiv:0804.1682}}, - NUMBER = {3}, - PAGES = {397--424}, - ISSN = {0022-040X}, - MRCLASS = {53C26 (14D06 32J27 32Q15)}, - MRNUMBER = {2739808}, -MRREVIEWER = {Justin Sawon}, - URL = {http://projecteuclid.org/euclid.jdg/1292940689}, -} - -@article{MR2746347, - Author = {Boucksom, Sébastien and Eyssidieux, Philippe and Guedj, Vincent and Zeriahi, Ahmed}, - Date-Added = {2015-06-19 15:15:17 +0000}, - Date-Modified ={2015-06-19 15:17:58 +0000}, - Journal = {Acta Math.}, - Number = 2, - Pages = {199--262}, - Title = {Monge-Ampère equations in big cohomology classes}, - Note = {\href{https://doi.org/10.1007/s11511-010-0054-7}{DOI:10.1007/s11511-010-0054-7}}, - Volume = 205, - Year = 2010 -} - -@book{MR2766102, - Author = {Lee, John M.}, - Doi = {10.1007/978-1-4419-7940-7}, - Edition = {Second}, - Isbn = {978-1-4419-7939-1}, - Mrclass = {57-01 (54-01 55-01)}, - Mrnumber = {2766102 (2011i:57001)}, - NOTE = - {\href{https://doi.org/10.1007/978-1-4419-7940-7}{DOI:10.1007/978-1-4419-7940-7}}, - Pages = {xviii+433}, - Publisher = {Springer, New York}, - Series = {Graduate Texts in Mathematics}, - Title = {Introduction to topological manifolds}, - Url = {https://doi.org/10.1007/978-1-4419-7940-7}, - Volume = 202, - Year = 2011, - Bdsk-Url-1 = {https://doi.org/10.1007/978-1-4419-7940-7} -} - -@article{MR2773396, - Author = {Biswas, Indranil and Dey, Arijit}, - Coden = {BSMQA9}, - Doi = {10.1016/j.bulsci.2010.10.001}, - Fjournal = {Bulletin des Sciences Mathématiques}, - Issn = {0007-4497}, - Journal = {Bull. Sci. Math.}, - Mrclass = {14J60 (14D20)}, - Mrnumber = {2773396 (2012b:14085)}, - Mrreviewer = {Zhenbo Qin}, - Number = 2, - Pages = {178--186}, - Note = {\href{https://doi.org/10.1016/j.bulsci.2010.10.001}{DOI: - 10.1016/j.bulsci.2010.10.001}}, - Title = {Bogomolov restriction theorem for {H}iggs bundles}, - Url = {https://doi.org/10.1016/j.bulsci.2010.10.001}, - Volume = 135, - Year = 2011, - Bdsk-Url-1 = {https://doi.org/10.1016/j.bulsci.2010.10.001} -} - -@incollection {MR2779470, - AUTHOR = {Campana, Frédéric}, - TITLE = {Special orbifolds and birational classification: a survey}, - BOOKTITLE = {Classification of algebraic varieties}, - SERIES = {EMS Ser. Congr. Rep.}, - PAGES = {123--170}, - PUBLISHER = {Eur. Math. Soc., Zürich}, - YEAR = {2011}, - MRCLASS = {14E05 (14-02 14E30)}, - MRNUMBER = {2779470}, -MRREVIEWER = {Alexandr V. Pukhlikov}, - NOTE = {\href{https://doi.org/10.4171/007-1/6}{DOI:10.4171/007-1/6}. Preprint \href{https://arXiv.org/abs/1001.3763v1}{arXiv:1001.3763v1}}, - DOI = {10.4171/007-1/6}, - URL = {https://doi.org/10.4171/007-1/6}, -} - -@article {MR2784026, - AUTHOR = {Choi, Sung Rak and Shokurov, Vyacheslav V.}, - TITLE = {Geography of log models: theory and applications}, - JOURNAL = {Cent. Eur. J. Math.}, - FJOURNAL = {Central European Journal of Mathematics}, - VOLUME = {9}, - YEAR = {2011}, - NUMBER = {3}, - Note = {\href{https://doi.org/10.2478/s11533-011-0013-3}{DOI:10.2478/s11533-011-0013-3}}, - PAGES = {489--534}, - ISSN = {1895-1074}, - MRCLASS = {14E30}, - MRNUMBER = {2784026}, -MRREVIEWER = {Vladimir Lazi\'{c}}, - DOI = {10.2478/s11533-011-0013-3}, - URL = {https://doi.org/10.2478/s11533-011-0013-3}, -} - -@article{MR2793040, - Author = {Biswas, Indranil and Dey, Arijit}, - Coden = {BSMQA9}, - Doi = {10.1016/j.bulsci.2010.04.003}, - Fjournal = {Bulletin des Sciences Mathématiques}, - Issn = {0007-4497}, - Journal = {Bull. Sci. Math.}, - Mrclass = {14F05 (14D20 14J60 14L15)}, - Mrnumber = {2793040 (2012h:14035)}, - Note = - {\href{https://doi.org/10.1016/j.bulsci.2010.04.003}{DOI:10.1016/j.bulsci.2010.04.003}}, - Mrreviewer = {Johan A. Martens}, - Number = 3, - Pages = {251--261}, - Title = {Restriction theorems for {H}iggs principal bundles}, - Url = {https://doi.org/10.1016/j.bulsci.2010.04.003}, - Volume = 135, - Year = 2011, - Bdsk-Url-1 = {https://doi.org/10.1016/j.bulsci.2010.04.003} -} - -@article{MR2796069, - Author = {Källström, Rolf}, - Coden = {JALGA4}, - Doi = {10.1016/j.jalgebra.2011.05.003}, - Fjournal = {Journal of Algebra}, - Issn = {0021-8693}, - Journal = {J. Algebra}, - Mrclass = {14A10 (14F05 14M10)}, - Mrnumber = {2796069 (2012d:14001)}, - Mrreviewer = {Ana Rita Martins}, - Pages = {169--180}, - Title = {The {Z}ariski-{L}ipman conjecture for complete intersections}, - Url = {https://doi.org/10.1016/j.jalgebra.2011.05.003}, - Volume = 337, - Year = 2011, - Bdsk-Url-1 = {https://doi.org/10.1016/j.jalgebra.2011.05.003} -} - -@inproceedings {MR2827803, - AUTHOR = {Hacon, Christopher D. and McKernan, James}, - TITLE = {Boundedness results in birational geometry}, - BOOKTITLE = {Proceedings of the {I}nternational {C}ongress of {M}athematicians. {V}olume {II}}, - PAGES = {427--449}, - PUBLISHER = {Hindustan Book Agency, New Delhi}, - YEAR = {2010}, - MRCLASS = {14E05 (14E30)}, - MRNUMBER = {2827803}, -MRREVIEWER = {Vladimir Lazić}, -} - -@article {MR2831280, - AUTHOR = {Campana, Frédéric}, - TITLE = {Orbifoldes géométriques spéciales et classification biméromorphe des variétés kählériennes compactes}, - JOURNAL = {J. Inst. Math. Jussieu}, - FJOURNAL = {Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Mathématiques de Jussieu}, - VOLUME = 10, - YEAR = 2011, - NOTE = {\href{https://doi.org/10.1017/S1474748010000101}{DOI:10.1017/S1474748010000101}. Preprint \href{http://arxiv.org/abs/0705.0737v5}{arXiv:0705.0737v5}.}, - NUMBER = 4, - PAGES = {809--934}, - ISSN = {1474-7480}, - MRCLASS = {32J27 (11G05 32J25 32Q45)}, - MRNUMBER = 2831280, - DOI = {10.1017/S1474748010000101}, - URL = {https://doi.org/10.1017/S1474748010000101}, -} - -@article {MR2838215, - AUTHOR = {Kollár, János}, - TITLE = {Simultaneous normalization and algebra husks}, - JOURNAL = {Asian J. Math.}, - FJOURNAL = {Asian Journal of Mathematics}, - VOLUME = 15, - YEAR = 2011, - NUMBER = 3, - NOTE = - {\href{https://doi.org/10.4310/AJM.2011.v15.n3.a6}{DOI:10.4310/AJM.2011.v15.n3.a6}. Preprint - \href{http://arxiv.org/abs/0910.1076}{arXiv:0910.1076}.}, - PAGES = {437--449}, - ISSN = {1093-6106}, - MRCLASS = {14B25 (14D06 14D15 14D22)}, - MRNUMBER = 2838215, - MRREVIEWER = {Liam O'Carroll}, - DOI = {10.4310/AJM.2011.v15.n3.a6}, - URL = {https://doi.org/10.4310/AJM.2011.v15.n3.a6}, -} - -@article{MR2860268, - Author = {Jabbusch, Kelly and Kebekus, Stefan}, - Coden = {MAZEAX}, - Doi = {10.1007/s00209-010-0758-6}, - Fjournal = {Mathematische Zeitschrift}, - Issn = {0025-5874}, - Journal = {Math. Z.}, - Mrclass = {14J10 (14D06 14D20)}, - Mrnumber = {2860268 (2012k:14046)}, - Mrreviewer = {Daniel Greb}, - Number = {3-4}, - Pages = {847--878}, - Title = {Families over special base manifolds and a conjecture of - {C}ampana}, - Note = - {\href{https://doi.org/10.1007/s00209-010-0758-6}{DOI:10.1007/s00209-010-0758-6}. Preprint - \href{https://arxiv.org/abs/0905.1746}{arXiv:0905.1746}}, - Volume = 269, - Year = 2011, - Bdsk-Url-1 = {https://doi.org/10.1007/s00209-010-0758-6} -} - -@article{MR2871152, - Author = {Patakfalvi, Zsolt}, - Coden = {ADMTA4}, - Doi = {10.1016/j.aim.2011.12.013}, - Fjournal = {Advances in Mathematics}, - Issn = {0001-8708}, - Journal = {Adv. Math.}, - Mrclass = {14J10 (14E05)}, - Mrnumber = {2871152 (2012m:14072)}, - Mrreviewer = {Atsushi Moriwaki}, - Number = 3, - Pages = {1640--1642}, - Title = {Viehweg's hyperbolicity conjecture is true over compact bases}, - Url = {https://doi.org/10.1016/j.aim.2011.12.013}, - Volume = 229, - Year = 2012, - Bdsk-Url-1 = {https://doi.org/10.1016/j.aim.2011.12.013} -} - -@article{MR2881306, - Author = {Peternell, Thomas}, - Doi = {10.4171/JEMS/312}, - Fjournal = {Journal of the European Mathematical Society (JEMS)}, - Issn = {1435-9855}, - Journal = {J. Eur. Math. Soc. (JEMS)}, - Mrclass = {14J10 (14C20 14E30 14J60)}, - Mrnumber = 2881306, - Mrreviewer = {Maria Chiara Brambilla}, - Number = 2, - Pages = {571--603}, - Title = {Varieties with generically nef tangent bundles}, - Url = {https://doi.org/10.4171/JEMS/312}, - Volume = 14, - Year = 2012, - Bdsk-Url-1 = {https://doi.org/10.4171/JEMS/312} -} - -@book {MR2883440, - AUTHOR = {Nicolaescu, Liviu}, - TITLE = {An invitation to {M}orse theory}, - SERIES = {Universitext}, - EDITION = {Second}, - PUBLISHER = {Springer, New York}, - NOTE = {\href{https://doi.org/10.1007/978-1-4614-1105-5}{DOI:10.1007/978-1-4614-1105-5}}, - YEAR = {2011}, - PAGES = {xvi+353}, - ISBN = {978-1-4614-1104-8}, - MRCLASS = {58E05 (37D15 37J15 57R45 57R70 58K05)}, - MRNUMBER = {2883440}, - DOI = {10.1007/978-1-4614-1105-5}, - URL = {https://doi.org/10.1007/978-1-4614-1105-5}, -} - -@incollection{MR2894633, - Address = {Providence, RI}, - Author = {Balaji, V. and Kollár, János}, - Booktitle = {Compact moduli spaces and vector bundles}, - Doi = {10.1090/conm/564/11154}, - Mrclass = {14J60 (14C05 14F05 32L05 32Q26)}, - Mrnumber = 2894633, - Mrreviewer = {Carlo Giovanni Madonna}, - Pages = {177--184}, - Publisher = {Amer. Math. Soc.}, - Series = {Contemp. Math.}, - Title = {Restrictions of stable bundles}, - Note = {\href{https://doi.org/10.1090/conm/564/11154}{DOI:10.1090/conm/564/11154}}, - Url = {https://doi.org/10.1090/conm/564/11154}, - Volume = 564, - Year = 2012, - Bdsk-Url-1 = {https://doi.org/10.1090/conm/564/11154} -} - -@article {MR2912485, - AUTHOR = {Yu, JianMing and Jiang, GuangFeng}, - TITLE = {Reducibility of finite reflection groups}, - JOURNAL = {Sci. China Math.}, - FJOURNAL = {Science China. Mathematics}, - VOLUME = {55}, - YEAR = {2012}, - NUMBER = {5}, - PAGES = {947--948}, - ISSN = {1674-7283}, - MRCLASS = {20F55 (52C35)}, - MRNUMBER = {2912485}, - NOTE = {\href{https://doi.org/10.1007/s11425-011-4341-3}{DOI:10.1007/s11425-011-4341-3}}, - DOI = {10.1007/s11425-011-4341-3}, - URL = {https://doi.org/10.1007/s11425-011-4341-3}, -} - -@article {MR2915479, - AUTHOR = {Greb, Daniel and Rollenske, Sönke}, - TITLE = {Torsion and cotorsion in the sheaf of {K}ähler differentials on some mild singularities}, - JOURNAL = {Math. Res. Lett.}, - FJOURNAL = {Mathematical Research Letters}, - VOLUME = 18, - YEAR = 2011, - NUMBER = 6, - PAGES = {1259--1269}, - ISSN = {1073-2780}, - MRCLASS = {14F10 (13N05 14B05)}, - MRNUMBER = 2915479, - MRREVIEWER = {Wenliang Zhang}, - NOTE = - {\href{https://doi.org/10.4310/MRL.2011.v18.n6.a14}{DOI:10.4310/MRL.2011.v18.n6.a14}. Preprint - \href{http://arxiv.org/abs/1012.5940}{arXiv:1012.5940}}, - DOI = {10.4310/MRL.2011.v18.n6.a14}, - URL = {https://doi.org/10.4310/MRL.2011.v18.n6.a14}, -} - -@article {MR2918165, - AUTHOR = {Höring, Andreas and Voisin, Claire}, - TITLE = {Anticanonical divisors and curve classes on {F}ano manifolds}, - JOURNAL = {Pure Appl. Math. Q.}, - FJOURNAL = {Pure and Applied Mathematics Quarterly}, - VOLUME = 7, - YEAR = 2011, - NOTE = {\href{https://doi.org/10.4310/PAMQ.2011.v7.n4.a13}{DOI:10.4310/PAMQ.2011.v7.n4.a13}.}, - NUMBER = {4, Special Issue: In memory of Eckart Viehweg}, - PAGES = {1371--1393}, - ISSN = {1558-8599}, - MRCLASS = {14J45 (14C30 14D07 14J17)}, - MRNUMBER = 2918165, - MRREVIEWER = {Carlo Giovanni Madonna}, - DOI = {10.4310/PAMQ.2011.v7.n4.a13}, - URL = {https://doi.org/10.4310/PAMQ.2011.v7.n4.a13}, -} - -@article {MR2918179, - AUTHOR = {Simpson, Carlos}, - TITLE = {Local systems on proper algebraic {$V$}-manifolds}, - JOURNAL = {Pure Appl. Math. Q.}, - FJOURNAL = {Pure and Applied Mathematics Quarterly}, - VOLUME = 7, - YEAR = 2011, - NUMBER = {4, Special Issue: In memory of Eckart Viehweg}, - PAGES = {1675--1759}, - ISSN = {1558-8599}, - MRCLASS = {14D23 (14A20 14C30 32C18)}, - MRNUMBER = 2918179, - MRREVIEWER = {Jack Hall}, - URL = {https://doi.org/10.4310/PAMQ.2011.v7.n4.a27}, -} - -@incollection{MR2931877, - Address = {Cambridge}, - Author = {Totaro, Burt}, - Booktitle = {Current developments in algebraic geometry}, - Mrclass = {14Jxx (30F35 30F45)}, - Mrnumber = 2931877, - Note = {preprint - \href{http://arxiv.org/abs/1008.3825}{arXiv:1008.3825}}, - Pages = {405--426}, - Publisher = {Cambridge Univ. Press}, - Series = {Math. Sci. Res. Inst. Publ.}, - Title = {Algebraic surfaces and hyperbolic geometry}, - Volume = 59, - Year = 2012 -} - -@article {MR2944479, - AUTHOR = {Fujino, Osamu and Gongyo, Yoshinori}, - TITLE = {On canonical bundle formulas and subadjunctions}, - JOURNAL = {Michigan Math. J.}, - FJOURNAL = {Michigan Mathematical Journal}, - VOLUME = {61}, - YEAR = {2012}, - NUMBER = {2}, - PAGES = {255--264}, - ISSN = {0026-2285}, - MRCLASS = {14C20 (14B05)}, - MRNUMBER = {2944479}, -MRREVIEWER = {Cícero Carvalho}, - NOTE = {\href{https://doi.org/10.1307/mmj/1339011526}{DOI:10.1307/mmj/1339011526}. Preprint \href{https://arxiv.org/abs/1009.3996}{arXiv:1009.3996}}, - DOI = {10.1307/mmj/1339011526}, - URL = {https://doi.org/10.1307/mmj/1339011526}, -} - -@article{MR2976311, - Author = {Jabbusch, Kelly and Kebekus, Stefan}, - Coden = {AIFUA7}, - Doi = {10.5802/aif.2673}, - Fjournal = {Université de Grenoble. Annales de l'Institut Fourier}, - Issn = {0373-0956}, - Journal = {Ann. Inst. Fourier (Grenoble)}, - Mrclass = {14D22 (14D07)}, - Mrnumber = 2976311, - Number = 6, - Pages = {2277--2290 (2012)}, - Title = {Positive sheaves of differentials coming from coarse moduli - spaces}, - Note = - {\href{https://doi.org/10.5802/aif.2673}{DOI:10.5802/aif.2673}. Preprint - \href{https://arxiv.org/abs/0904.2445}{arXiv:0904.2445}.}, - Url = {https://doi.org/10.5802/aif.2673}, - Volume = 61, - Year = 2011, - Bdsk-Url-1 = {https://doi.org/10.5802/aif.2673} -} - -@article {MR3010808, - AUTHOR = {Odaka, Yuji}, - TITLE = {The {GIT} stability of polarized varieties via discrepancy}, - JOURNAL = {Ann. of Math. (2)}, - FJOURNAL = {Annals of Mathematics. Second Series}, - VOLUME = {177}, - YEAR = {2013}, - NUMBER = {2}, - PAGES = {645--661}, - ISSN = {0003-486X}, - MRCLASS = {14C20 (14J17 14L24 32Q26)}, - MRNUMBER = {3010808}, -MRREVIEWER = {Daniel Greb}, - NOTE = {\href{https://doi.org/10.4007/annals.2013.177.2.6}{DOI:10.4007/annals.2013.177.2.6}. Preprint \href{https://arxiv.org/abs/0807.1716}{arXiv:0807.1716}}, - DOI = {10.4007/annals.2013.177.2.6}, - URL = {https://doi.org/10.4007/annals.2013.177.2.6}, -} - -@article {MR3030002, - AUTHOR = {Höring, Andreas and Novelli, Carla}, - TITLE = {Mori contractions of maximal length}, - JOURNAL = {Publ. Res. Inst. Math. Sci.}, - FJOURNAL = {Publications of the Research Institute for Mathematical - Sciences}, - VOLUME = 49, - YEAR = 2013, - NOTE = {\href{https://doi.org/10.4171/PRIMS/103}{DOI:10.4171/PRIMS/103}. Preprint \href{http://arxiv.org/abs/1201.4009}{arXiv:1201.4009}.}, - NUMBER = 1, - PAGES = {215--228}, - ISSN = {0034-5318}, - MRCLASS = {14E30 (14D06 14J45)}, - MRNUMBER = 3030002, - MRREVIEWER = {Zhi Jiang}, - DOI = {10.4171/PRIMS/103}, - URL = {https://doi.org/10.4171/PRIMS/103}, -} - -@article{MR3030068, - Author = {Jahnke, Priska and Radloff, Ivo}, - Doi = {10.1142/S0129167X12501224}, - Fjournal = {International Journal of Mathematics}, - Issn = {0129-167X}, - Journal = {Internat. J. Math.}, - Mrclass = {32Q26 (14E20 14E30 32J27 32L10)}, - Mrnumber = 3030068, - Mrreviewer = {G. K. Sankaran}, - Number = 1, - NOTE = {\href{https://doi.org/10.1142/S0129167X12501224}{DOI:10.1142/S0129167X12501224}. Preprint \href{http://arxiv.org/abs/1106.1300}{arXiv:1106.1300}.}, - Pages = {1250122, 15}, - Title = {Semistability of restricted tangent bundles and a question of {I}. {B}iswas}, - Url = {https://doi.org/10.1142/S0129167X12501224}, - Volume = 24, - Year = 2013, - Bdsk-Url-1 = {https://doi.org/10.1142/S0129167X12501224} -} - -@article {MR3033631, - AUTHOR = {Araujo, Carolina and Druel, Stéphane}, - TITLE = {On {F}ano foliations}, - JOURNAL = {Adv. Math.}, - FJOURNAL = {Advances in Mathematics}, - VOLUME = {238}, - YEAR = {2013}, - PAGES = {70--118}, - NOTE = {\href{https://doi.org/10.1016/j.aim.2013.02.003}{DOI:10.1016/j.aim.2013.02.003}. Preprint \href{https://arxiv.org/abs/1112.4512}{arXiv:1112.4512}}, - ISSN = {0001-8708}, - MRCLASS = {37F25 (14M22)}, - MRNUMBER = {3033631}, - DOI = {10.1016/j.aim.2013.02.003}, - URL = {https://doi.org/10.1016/j.aim.2013.02.003}, -} - -@article {MR3034294, - AUTHOR = {Hacon, Christopher D. and McKernan, James and Xu, Chenyang}, - TITLE = {On the birational automorphisms of varieties of general type}, - JOURNAL = {Ann. of Math. (2)}, - FJOURNAL = {Annals of Mathematics. Second Series}, - VOLUME = 177, - YEAR = 2013, - NOTE = {\href{https://doi.org/10.4007/annals.2013.177.3.6}{DOI:10.4007/annals.2013.177.3.6}}, - NUMBER = 3, - PAGES = {1077--1111}, - ISSN = {0003-486X}, - MRCLASS = {14E05}, - MRNUMBER = 3034294, - MRREVIEWER = {Alexandr V. Pukhlikov}, - DOI = {10.4007/annals.2013.177.3.6}, - URL = {https://doi.org/10.4007/annals.2013.177.3.6}, -} - -@article {MR3044124, - AUTHOR = {Klingler, Bruno}, - TITLE = {Symmetric differentials, {K}ähler groups and ball quotients}, - JOURNAL = {Invent. Math.}, - FJOURNAL = {Inventiones Mathematicae}, - VOLUME = 192, - YEAR = 2013, - NOTE = - {\href{https://doi.org/10.1007/s00222-012-0411-6}{DOI:10.1007/s00222-012-0411-6}.}, - NUMBER = 2, - PAGES = {257--286}, - ISSN = {0020-9910}, - MRCLASS = {22E10 (22E45 32M05 32P05 32Q55)}, - MRNUMBER = 3044124, - MRREVIEWER = {Takashi Umeno}, - DOI = {10.1007/s00222-012-0411-6}, - URL = {https://doi.org/10.1007/s00222-012-0411-6}, -} - -@book {MR3057950, - AUTHOR = {Kollár, János}, - TITLE = {Singularities of the minimal model program}, - SERIES = {Cambridge Tracts in Mathematics}, - VOLUME = 200, - NOTE = {With a collaboration of Sándor - Kovács. \href{https://doi.org/10.1017/CBO9781139547895}{DOI:10.1017/CBO9781139547895}}, - PUBLISHER = {Cambridge University Press, Cambridge}, - YEAR = 2013, - PAGES = {x+370}, - ISBN = {978-1-107-03534-8}, - MRCLASS = {14E30 (14B05)}, - MRNUMBER = 3057950, - MRREVIEWER = {Tommaso De Fernex}, - DOI = {10.1017/CBO9781139547895}, - URL = {https://doi.org/10.1017/CBO9781139547895}, -} - -@article {MR3077660, - AUTHOR = {Lohmann, Daniel}, - TITLE = {Families of canonically polarized manifolds over log {F}ano varieties}, - JOURNAL = {Compos. Math.}, - FJOURNAL = {Compositio Mathematica}, - VOLUME = {149}, - YEAR = {2013}, - Note = {\href{https://doi.org/10.1112/S0010437X1200053X}{DOI:10.1112/S0010437X1200053X}}, - NUMBER = {6}, - PAGES = {1019--1040}, - ISSN = {0010-437X}, - MRCLASS = {14J10 (14E30)}, - MRNUMBER = {3077660}, -MRREVIEWER = {Atsushi Moriwaki}, - DOI = {10.1112/S0010437X1200053X}, - URL = {https://doi.org/10.1112/S0010437X1200053X}, -} - -@article{MR3084424, - Author = {Kebekus, Stefan}, - Doi = {10.1016/j.aim.2013.06.013}, - Fjournal = {Advances in Mathematics}, - Issn = {0001-8708}, - Journal = {Adv. Math.}, - Mrclass = {14J17 (14B05 14F10)}, - Mrnumber = 3084424, - Note = - {\href{https://doi.org/10.1016/j.aim.2013.06.013}{DOI:10.1016/j.aim.2013.06.013}. Preprint - \href{http://arxiv.org/abs/1210.3255}{arXiv:1210.3255}.}, - Pages = {78--112}, - Title = {Pull-back morphisms for reflexive differential forms}, - Url = {https://doi.org/10.1016/j.aim.2013.06.013}, - Volume = 245, - Year = 2013, - Bdsk-Url-1 = {https://doi.org/10.1016/j.aim.2013.06.013} -} - -@article {MR3087348, - AUTHOR = {Sabbah, Claude}, - TITLE = {Théorie de {H}odge et correspondance de {H}itchin-{K}obayashi - sauvages (d'après {T}. {M}ochizuki)}, - NOTE = {Séminaire Bourbaki. Vol. 2011/2012. Exposés 1043--1058}, - JOURNAL = {Astérisque}, - FJOURNAL = {Astérisque}, - NUMBER = 352, - YEAR = 2013, - PAGES = {Exp. No. 1050, viii, 205--241}, - ISSN = {0303-1179}, - ISBN = {978-2-85629-371-3}, - MRCLASS = {14C30 (14J60 32C38 53C07)}, - MRNUMBER = 3087348, - MRREVIEWER = {Ahmed Lesfari}, -} - -@incollection {MR3088903, - AUTHOR = {Eyssidieux, Philippe}, - TITLE = {Lectures on the {S}hafarevich conjecture on uniformization}, - BOOKTITLE = {Complex manifolds, foliations and uniformization}, - SERIES = {Panor. Synthèses}, - VOLUME = {34/35}, - PAGES = {101--148}, - PUBLISHER = {Soc. Math. France, Paris}, - YEAR = 2011, - MRCLASS = {32J25 (14F35 32E05 32Q30)}, - MRNUMBER = 3088903, - MRREVIEWER = {André Oliveira}, -} - -@article {MR3095099, - AUTHOR = {McQuillan, Michael}, - TITLE = {Dérivation relative}, - JOURNAL = {C. R. Math. Acad. Sci. Paris}, - FJOURNAL = {Comptes Rendus Mathématique. Académie des Sciences. Paris}, - VOLUME = 351, - YEAR = 2013, - NOTE = - {\href{https://doi.org/10.1016/j.crma.2013.05.003}{DOI:10.1016/j.crma.2013.05.003}}, - NUMBER = {13-14}, - PAGES = {523--526}, - ISSN = {1631-073X}, - MRCLASS = {14G40 (32P05 32U40)}, - MRNUMBER = 3095099, - DOI = {10.1016/j.crma.2013.05.003}, - URL = {https://doi.org/10.1016/j.crma.2013.05.003}, -} - -@article {MR3127814, - AUTHOR = {Brunebarbe, Yohan and Klingler, Bruno and Totaro, Burt}, - TITLE = {Symmetric differentials and the fundamental group}, - JOURNAL = {Duke Math. J.}, - FJOURNAL = {Duke Mathematical Journal}, - VOLUME = 162, - YEAR = 2013, - NOTE = {\href{https://doi.org/10.1215/00127094-2381442}{DOI:10.1215/00127094-2381442}.}, - NUMBER = 14, - PAGES = {2797--2813}, - ISSN = {0012-7094}, - MRCLASS = {14F35 (14D07 14F10)}, - MRNUMBER = 3127814, - MRREVIEWER = {Alex Degtyarev}, - DOI = {10.1215/00127094-2381442}, - URL = {https://doi.org/10.1215/00127094-2381442}, -} - -@article {MR3134683, - AUTHOR = {Campana, Frédéric and Guenancia, Henri and Păun, Mihai}, - TITLE = {Metrics with cone singularities along normal crossing divisors - and holomorphic tensor fields}, - JOURNAL = {Ann. Sci. Éc. Norm. Supér. (4)}, - FJOURNAL = {Annales Scientifiques de l'École Normale Supérieure. Quatrième - Série}, - VOLUME = 46, - YEAR = 2013, - NUMBER = 6, - PAGES = {879--916}, - ISSN = {0012-9593}, - MRCLASS = {32Q25 (14E05 53C55)}, - MRNUMBER = 3134683, - MRREVIEWER = {Hans-Joachim Hein}, -} - -@book {MR3156076, - AUTHOR = {Noguchi, Junjiro and Winkelmann, Jörg}, - TITLE = {Nevanlinna theory in several complex variables and {D}iophantine approximation}, - SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]}, - VOLUME = {350}, - PUBLISHER = {Springer, Tokyo}, - YEAR = {2014}, - PAGES = {xiv+416}, - ISBN = {978-4-431-54570-5; 978-4-431-54571-2}, - MRCLASS = {32-02 (11J25 11J97 32H30 32Q45)}, - MRNUMBER = {3156076}, -MRREVIEWER = {William A. Cherry}, - NOTE = {\href{https://doi.org/10.1007/978-4-431-54571-2}{DOI:10.1007/978-4-431-54571-2}}, - DOI = {10.1007/978-4-431-54571-2}, - URL = {https://doi.org/10.1007/978-4-431-54571-2}, -} - -@article{MR3170714, - Author = {Nemirovski, Stefan}, - Doi = {10.1080/17476933.2011.592579}, - Fjournal = {Complex Variables and Elliptic Equations. An International - Journal}, - Issn = {1747-6933}, - Journal = {Complex Var. Elliptic Equ.}, - Mrclass = {32E40 (32C55 32M05)}, - Mrnumber = 3170714, - Mrreviewer = {Viorel Vâjâitu}, - Number = 11, - Pages = {1517--1525}, - Title = {Levi problem and semistable quotients}, - Note = - {\href{https://doi.org/10.1080/17476933.2011.592579}{DOI:10.1080/17476933.2011.592579}}, - Url = {https://doi.org/10.1080/17476933.2011.592579}, - Volume = 58, - Year = 2013, - Bdsk-Url-1 = {https://doi.org/10.1080/17476933.2011.592579} -} - -@article {MR3224718, - AUTHOR = {Hacon, Christopher D. and McKernan, James and Xu, Chenyang}, - TITLE = {A{CC} for log canonical thresholds}, - JOURNAL = {Ann. of Math. (2)}, - FJOURNAL = {Annals of Mathematics. Second Series}, - VOLUME = 180, - YEAR = 2014, - NUMBER = 2, - PAGES = {523--571}, - ISSN = {0003-486X}, - MRCLASS = {14E05 (14C20 14E30)}, - MRNUMBER = 3224718, - MRREVIEWER = {Alexandr V. Pukhlikov}, - NOTE = - {\href{https://doi.org/10.4007/annals.2014.180.2.3}{DOI:10.4007/annals.2014.180.2.3}. Preprint - \href{http://arxiv.org/abs/1208.4150}{arXiv:1208.4150}}, - DOI = {10.4007/annals.2014.180.2.3}, - URL = {https://doi.org/10.4007/annals.2014.180.2.3}, -} - -@incollection {MR3229352, - AUTHOR = {Popov, Vladimir L.}, - TITLE = {Jordan groups and automorphism groups of algebraic varieties}, - BOOKTITLE = {Automorphisms in birational and affine geometry}, - SERIES = {Springer Proc. Math. Stat.}, - VOLUME = {79}, - PAGES = {185--213}, - PUBLISHER = {Springer, Cham}, - YEAR = {2014}, - NOTE = {\href{https://doi.org/10.1007/978-3-319-05681-4_11}{DOI:10.1007/978-3-319-05681-4$\_$11}}, - MRCLASS = {14E07 (14J50 20E07)}, - MRNUMBER = {3229352}, -MRREVIEWER = {Ilya Karzhemanov}, - DOI = {10.1007/978-3-319-05681-4_11}, - URL = {https://doi.org/10.1007/978-3-319-05681-4_11}, -} - -@article {MR3247804, - AUTHOR = {Graf, Patrick and Kovács, Sándor J.}, - TITLE = {An optimal extension theorem for 1-forms and the {L}ipman-{Z}ariski conjecture}, - JOURNAL = {Doc. Math.}, - FJOURNAL = {Documenta Mathematica}, - VOLUME = 19, - YEAR = 2014, - PAGES = {815--830}, - ISSN = {1431-0635}, - MRCLASS = {14B05 (32S05)}, - MRNUMBER = 3247804, - MRREVIEWER = {Carles Bivià-Ausina}, - Note = {Preprint - \href{http://arxiv.org/abs/1301.7315}{arXiv:1301.7315}}, -} - -@article {MR3272910, - AUTHOR = {Huber, Annette and Jörder, Clemens}, - TITLE = {Differential forms in the h-topology}, - JOURNAL = {Algebr. Geom.}, - FJOURNAL = {Algebraic Geometry}, - VOLUME = 1, - YEAR = 2014, - NUMBER = 4, - PAGES = {449--478}, - ISSN = {2214-2584}, - MRCLASS = {14F10 (14F05 14F40 14J17)}, - MRNUMBER = 3272910, - MRREVIEWER = {Patrick Graf}, - NOTE = - {\href{https://doi.org/10.14231/AG-2014-020}{DOI:10.14231/AG-2014-020}. 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Z.}, - FJOURNAL = {Mathematische Zeitschrift}, - VOLUME = 278, - YEAR = 2014, - NOTE = - {\href{https://doi.org/10.1007/s00209-014-1337-z}{DOI:10.1007/s00209-014-1337-z}. Preprint - \href{http://arxiv.org/abs/1311.5141}{arXiv:1311.5141}}, - NUMBER = {3-4}, - PAGES = {893--899}, - ISSN = {0025-5874}, - MRCLASS = {32C15 (14F10 32C20 32S05)}, - MRNUMBER = 3278896, - MRREVIEWER = {Christian Lehn}, - DOI = {10.1007/s00209-014-1337-z}, - URL = {https://doi.org/10.1007/s00209-014-1337-z}, -} - -@article {MR3283927, - AUTHOR = {Berman, Robert J. and Guenancia, Henri}, - TITLE = {Kähler-{E}instein metrics on stable varieties and log canonical pairs}, - JOURNAL = {Geom. Funct. Anal.}, - FJOURNAL = {Geometric and Functional Analysis}, - VOLUME = 24, - YEAR = 2014, - NUMBER = 6, - NOTE = {\href{https://doi.org/10.1007/s00039-014-0301-8}{DOI:10.1007/s00039-014-0301-8}. 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Preprint \href{https://arxiv.org/abs/1311.7396}{arXiv:1311.7396}}, - DOI = {10.1016/j.aim.2014.10.023}, - URL = {https://doi.org/10.1016/j.aim.2014.10.023}, -} - -@article {MR3292293, - AUTHOR = {Prokhorov, Yuri G. and Shramov, Constantin}, - TITLE = {Jordan property for groups of birational selfmaps}, - JOURNAL = {Compos. Math.}, - FJOURNAL = {Compositio Mathematica}, - VOLUME = 150, - YEAR = 2014, - NOTE = - {\href{https://doi.org/10.1112/S0010437X14007581}{DOI:10.1112/S0010437X14007581}. 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Math.}, - Mrclass = {14G17 (14F05 14J60)}, - Mrnumber = 3314517, - Note = - {\href{https://doi.org/10.1007/s00222-014-0534-z}{DOI:10.1007/s00222-014-0534-z}}, - Number = 3, - Pages = {889--920}, - Title = {Bogomolov's inequality for {H}iggs sheaves in positive - characteristic}, - Url = {https://doi.org/10.1007/s00222-014-0534-z}, - Volume = 199, - Year = 2015, - Bdsk-Url-1 = {https://doi.org/10.1007/s00222-014-0534-z} -} - -@article {MR3314830, - AUTHOR = {Campana, Fréderic and Claudon, Benoît and Eyssidieux, Philippe}, - TITLE = {Représentations linéaires des groupes kählériens: factorisations et conjecture de {S}hafarevich linéaire}, - JOURNAL = {Compos. Math.}, - FJOURNAL = {Compositio Mathematica}, - VOLUME = 151, - YEAR = 2015, - NOTE = {\href{https://doi.org/10.1112/S0010437X14007751}{DOI:10.1112/S0010437X14007751}. 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Mathematics}, - VOLUME = 58, - YEAR = 2015, - NOTE = - {\href{https://doi.org/10.1007/s11425-014-4927-7}{DOI:10.1007/s11425-014-4927-7}.}, - NUMBER = 3, - PAGES = {531--542}, - ISSN = {1674-7283}, - MRCLASS = {14D06 (14E30)}, - MRNUMBER = 3319924, - MRREVIEWER = {Alan Matthew Thompson}, - DOI = {10.1007/s11425-014-4927-7}, - URL = {https://doi.org/10.1007/s11425-014-4927-7}, -} - -@book {MR3328860, - AUTHOR = {Brunella, Marco}, - TITLE = {Birational geometry of foliations}, - SERIES = {IMPA Monographs}, - VOLUME = 1, - PUBLISHER = {Springer, Cham}, - YEAR = 2015, - PAGES = {xiv+130}, - ISBN = {978-3-319-14309-5; 978-3-319-14310-1}, - MRCLASS = {14E05 (32C35 32J25 32S65 37F75)}, - MRNUMBER = 3328860, - NOTE = {\href{https://doi.org/10.1007/978-3-319-14310-1}{DOI:10.1007/978-3-319-14310-1}.}, - DOI = {10.1007/978-3-319-14310-1}, - URL = {https://doi.org/10.1007/978-3-319-14310-1}, -} - -@article {MR3329677, - AUTHOR = {Fujino, Osamu and Gongyo, Yoshinori}, - TITLE = {On the moduli b-divisors of lc-trivial fibrations}, - JOURNAL = {Ann. Inst. Fourier (Grenoble)}, - FJOURNAL = {Université de Grenoble. Annales de l'Institut Fourier}, - VOLUME = 64, - YEAR = 2014, - NOTE = {URL \url{http://aif.cedram.org/item?id=AIF_2014__64_4_1721_0}}, - NUMBER = 4, - PAGES = {1721--1735}, - ISSN = {0373-0956}, - MRCLASS = {14J10 (14E30 14N30)}, - MRNUMBER = 3329677, -MRREVIEWER = {Enrica Floris}, - URL = {http://aif.cedram.org/item?id=AIF_2014__64_4_1721_0}, -} - -@book {MR3330490, - AUTHOR = {Cox, David A. and Little, John and O'Shea, Donal}, - TITLE = {Ideals, varieties, and algorithms}, - SERIES = {Undergraduate Texts in Mathematics}, - EDITION = {Fourth}, - NOTE = {An introduction to computational algebraic geometry and commutative algebra. \href{https://doi.org/10.1007/978-3-319-16721-3}{DOI:10.1007/978-3-319-16721-3}}, - PUBLISHER = {Springer, Cham}, - YEAR = {2015}, - PAGES = {xvi+646}, - ISBN = {978-3-319-16720-6; 978-3-319-16721-3}, - MRCLASS = {13P10 (13-01 14-01 14Qxx 68W30)}, - MRNUMBER = {3330490}, - DOI = {10.1007/978-3-319-16721-3}, - URL = {https://doi.org/10.1007/978-3-319-16721-3}, -} - -@incollection {MR3331401, - AUTHOR = {Yamanoi, Katsutoshi}, - TITLE = {Kobayashi hyperbolicity and higher-dimensional {N}evanlinna theory}, - BOOKTITLE = {Geometry and analysis on manifolds}, - SERIES = {Progr. Math.}, - VOLUME = {308}, - PAGES = {209--273}, - PUBLISHER = {Birkhäuser/Springer, Cham}, - YEAR = {2015}, - MRCLASS = {32Q45 (32H30)}, - MRNUMBER = {3331401}, -MRREVIEWER = {Pei-Chu Hu}, - NOTE = {\href{https://doi.org/10.1007/978-3-319-11523-8_9}{DOI:10.1007/978-3-319-11523-8\_9}}, - DOI = {10.1007/978-3-319-11523-8_9}, - URL = {https://doi.org/10.1007/978-3-319-11523-8_9}, -} - -@article {MR3343876, - AUTHOR = {Graf, Patrick}, - TITLE = {The generalized {L}ipman-{Z}ariski problem}, - JOURNAL = {Math. Ann.}, - FJOURNAL = {Mathematische Annalen}, - VOLUME = 362, - YEAR = 2015, - Note = {\href{https://doi.org/10.1007/s00208-014-1112-9}{DOI:10.1007/s00208-014-1112-9}. Preprint \href{http://arxiv.org/abs/1405.1244}{arXiv:1405.1244}}, - NUMBER = {1-2}, - PAGES = {241--264}, - ISSN = {0025-5831}, - MRCLASS = {14B05 (14F10 32S05 32S25)}, - MRNUMBER = 3343876, - MRREVIEWER = {K. Kiyek}, - DOI = {10.1007/s00208-014-1112-9}, - URL = {https://doi.org/10.1007/s00208-014-1112-9}, -} - -@incollection {MR3380453, - AUTHOR = {Kollár, János}, - TITLE = {Deformations of elliptic {C}alabi-{Y}au manifolds}, - BOOKTITLE = {Recent advances in algebraic geometry}, - Note = - {\href{https://doi.org/10.1017/CBO9781107416000.015}{DOI:10.1017/CBO9781107416000.015}. Preprint - \href{http://arxiv.org/abs/1206.5721}{arXiv:1206.5721}}, - SERIES = {London Math. Soc. Lecture Note Ser.}, - VOLUME = 417, - PAGES = {254--290}, - PUBLISHER = {Cambridge Univ. Press, Cambridge}, - YEAR = 2015, - MRCLASS = {14J32}, - MRNUMBER = 3380453, -} - -@article {MR3483470, - AUTHOR = {Prokhorov, Yuri G. and Shramov, Constantin}, - TITLE = {Jordan property for {C}remona groups}, - JOURNAL = {Amer. J. Math.}, - FJOURNAL = {American Journal of Mathematics}, - VOLUME = 138, - YEAR = 2016, - NOTE = {\href{https://doi.org/10.1353/ajm.2016.0017}{DOI:10.1353/ajm.2016.0017}. Preprint \href{https://arxiv.org/abs/1211.3563}{arXiv:math/1211.3563}}, - NUMBER = 2, - PAGES = {403--418}, - ISSN = {0002-9327}, - MRCLASS = {14E07}, - MRNUMBER = 3483470, - MRREVIEWER = {Zinovy Reichstein}, - DOI = {10.1353/ajm.2016.0017}, - URL = {https://doi.org/10.1353/ajm.2016.0017}, -} - -@article {MR3502099, - AUTHOR = {Birkar, Caucher and Zhang, De-Qi}, - TITLE = {Effectivity of {I}itaka fibrations and pluricanonical systems of polarized pairs}, - JOURNAL = {Publ. Math. Inst. Hautes Études Sci.}, - FJOURNAL = {Publications Mathématiques. Institut de Hautes Études Scientifiques}, - VOLUME = 123, - YEAR = 2016, - PAGES = {283--331}, - ISSN = {0073-8301}, - NOTE = {\href{https://doi.org/10.1007/s10240-016-0080-x}{DOI:10.1007/s10240-016-0080-x}}, - MRCLASS = {14E05 (14E30)}, - MRNUMBER = 3502099, - MRREVIEWER = {Alex Massarenti}, - DOI = {10.1007/s10240-016-0080-x}, - URL = {https://doi.org/10.1007/s10240-016-0080-x}, -} - -@article {MR3507257, - AUTHOR = {Hacon, Christopher D. and Xu, Chenyang}, - TITLE = {Boundedness of log {C}alabi-{Y}au pairs of {F}ano type}, - JOURNAL = {Math. Res. Lett.}, - FJOURNAL = {Mathematical Research Letters}, - VOLUME = 22, - YEAR = 2015, - NOTE = {\href{https://doi.org/10.4310/MRL.2015.v22.n6.a8}{DOI:10.4310/MRL.2015.v22.n6.a8}}, - NUMBER = 6, - PAGES = {1699--1716}, - ISSN = {1073-2780}, - MRCLASS = {14E05}, - MRNUMBER = 3507257, - MRREVIEWER = {Lei Zhang}, - DOI = {10.4310/MRL.2015.v22.n6.a8}, - URL = {https://doi.org/10.4310/MRL.2015.v22.n6.a8}, -} - -@article {MR3520712, - AUTHOR = {Graf, Patrick}, - TITLE = {A {M}ehta-{R}amanathan theorem for linear systems with - basepoints}, - JOURNAL = {Math. Nachr.}, - FJOURNAL = {Mathematische Nachrichten}, - VOLUME = 289, - YEAR = 2016, - Note = - {\href{https://doi.org/10.1002/mana.201500180}{DOI:10.1002/mana.201500180}. Preprint - \href{http://arxiv.org/abs/1501.04210}{arXiv:1501.04210}}, - NUMBER = 10, - PAGES = {1208--1218}, - ISSN = {0025-584X}, - MRCLASS = {14C20 (14H60 14J60)}, - MRNUMBER = 3520712, - DOI = {10.1002/mana.201500180}, - URL = {https://doi.org/10.1002/mana.201500180}, -} - -@article {MR3556423, - AUTHOR = {Ambro, Florin}, - TITLE = {Variation of log canonical thresholds in linear systems}, - JOURNAL = {Int. Math. Res. Not. IMRN}, - FJOURNAL = {International Mathematics Research Notices. IMRN}, - YEAR = {2016}, - Note = {\href{https://doi.org/10.1093/imrn/rnv284}{DOI:10.1093/imrn/rnv284}}, - NUMBER = {14}, - PAGES = {4418--4448}, - ISSN = {1073-7928}, - MRCLASS = {14E30 (14J45 14M25)}, - MRNUMBER = {3556423}, -MRREVIEWER = {Alex Massarenti}, - DOI = {10.1093/imrn/rnv284}, - URL = {https://doi.org/10.1093/imrn/rnv284}, -} - -@article {MR3580792, - AUTHOR = {Huber, Annette}, - TITLE = {Differential forms in algebraic geometry---a new perspective in the singular case}, - JOURNAL = {Port. Math.}, - FJOURNAL = {Portugaliae Mathematica. A Journal of the Portuguese - Mathematical Society}, - VOLUME = 73, - YEAR = 2016, - NOTE = {\href{https://doi.org/10.4171/PM/1990}{DOI:10.4171/PM/1990}}, - NUMBER = 4, - PAGES = {337--367}, - ISSN = {0032-5155}, - MRCLASS = {14F10 (14F20 14J17 58A10)}, - MRNUMBER = 3580792, - DOI = {10.4171/PM/1990}, - URL = {https://doi.org/10.4171/PM/1990}, -} - -@article {MR3604863, - AUTHOR = {Tian, Zhiyu and Xu, Chenyang}, - TITLE = {Finiteness of fundamental groups}, - JOURNAL = {Compos. Math.}, - FJOURNAL = {Compositio Mathematica}, - NOTE = {\href{https://doi.org/10.1112/S0010437X16007867}{DOI:10.1112/S0010437X16007867}. Preprint \href{http://arxiv.org/abs/1508.04536}{arXiv:1508.04536}.}, - VOLUME = {153}, - YEAR = {2017}, - NUMBER = {2}, - PAGES = {257--273}, - ISSN = {0010-437X}, - MRCLASS = {14B05 (14J45 32S50)}, - MRNUMBER = {3604863}, -MRREVIEWER = {Ilya Karzhemanov}, - DOI = {10.1112/S0010437X16007867}, - URL = {https://doi.org/10.1112/S0010437X16007867}, -} - -@incollection {MR3666021, - AUTHOR = {Claudon, Benoît}, - TITLE = {Positivité du cotangent logarithmique et conjecture de {S}hafarevich-{V}iehweg}, - NOTE = {Séminaire Bourbaki. Vol. 2015/2016. Exposés 1104--1119. Available on the internet at \href{https://smf.emath.fr/publications/expose-1105-positivite-du-cotangent-logarithmique-et-conjecture-de-shafarevich-viehweg}{this url}. Preprint \href{http://arxiv.org/abs/1603.09568}{arXiv:1603.09568}}, - JOURNAL = {Astérisque}, - FJOURNAL = {Astérisque}, - NUMBER = {390}, - YEAR = {2017}, - PAGES = {Exp. No. 1105, 27--63}, - ISSN = {0303-1179}, - ISBN = {978-2-85629-855-8}, - MRCLASS = {14D22 (32J25 32S65)}, - MRNUMBER = {3666021}, -MRREVIEWER = {Ahmed Lesfari}, -} - -@incollection {MR3675465, - AUTHOR = {Wentworth, Richard A.}, - TITLE = {Higgs bundles and local systems on {R}iemann surfaces}, - BOOKTITLE = {Geometry and quantization of moduli spaces}, - SERIES = {Adv. Courses Math. CRM Barcelona}, - PAGES = {165--219}, - PUBLISHER = {Birkhäuser/Springer, Cham}, - YEAR = 2016, - MRCLASS = {14H60 (32L10)}, - MRNUMBER = 3675465, -} - -@article {MR3715691, - AUTHOR = {Fujita, Kento}, - TITLE = {Examples of {K}-unstable {F}ano manifolds with the {P}icard number 1}, - JOURNAL = {Proc. Edinb. Math. Soc. (2)}, - FJOURNAL = {Proceedings of the Edinburgh Mathematical Society. Series II}, - VOLUME = {60}, - YEAR = {2017}, - NUMBER = {4}, - PAGES = {881--891}, - ISSN = {0013-0915}, - MRCLASS = {14J45 (14L24)}, - MRNUMBER = {3715691}, -MRREVIEWER = {Jesus Martinez-Garcia}, - NOTE = {\href{https://doi.org/10.1017/S0013091516000432}{DOI:10.1017/S0013091516000432}. Preprint \href{https://arxiv.org/abs/1508.04290}{arXiv:1508.04290}}, - DOI = {10.1017/S0013091516000432}, - URL = {https://doi.org/10.1017/S0013091516000432}, -} - -@article {MR3731324, - AUTHOR = {Li, Chi}, - TITLE = {Yau-{T}ian-{D}onaldson correspondence for {K}-semistable {F}ano manifolds}, - JOURNAL = {J. Reine Angew. Math.}, - FJOURNAL = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]}, - VOLUME = {733}, - YEAR = {2017}, - PAGES = {55--85}, - ISSN = {0075-4102}, - MRCLASS = {32Q25 (53C55)}, - MRNUMBER = {3731324}, -MRREVIEWER = {Ruadha\'{\i} Dervan}, - NOTE = {\href{https://doi.org/10.1515/crelle-2014-0156}{DOI:10.1515/crelle-2014-0156}. Preprint \href{https://arxiv.org/abs/1302.6681}{arXiv:math/1302.6681}}, - DOI = {10.1515/crelle-2014-0156}, - URL = {https://doi.org/10.1515/crelle-2014-0156}, -} - -@article {MR3782691, - AUTHOR = {Favale, Filippo F.}, - TITLE = {Calabi-{Y}au quotients with terminal singularities}, - JOURNAL = {Boll. Unione Mat. Ital.}, - FJOURNAL = {Bollettino dell'Unione Matematica Italiana}, - VOLUME = {11}, - YEAR = {2018}, - NOTE = {\href{https://doi.org/10.1007/s40574-017-0128-y}{DOI:10.1007/s40574-017-0128-y}. Preprint \href{https://arxiv.org/abs/1306.3555}{arXiv:1306.3555}.}, - NUMBER = {1}, - PAGES = {55--67}, - ISSN = {1972-6724}, - MRCLASS = {14J32 (14J17 14J50)}, - MRNUMBER = {3782691}, -MRREVIEWER = {Nam-Hoon Lee}, - DOI = {10.1007/s40574-017-0128-y}, - URL = {https://doi.org/10.1007/s40574-017-0128-y}, -} - -@article {MR3783213, - AUTHOR = {Fujita, Kento}, - TITLE = {Optimal bounds for the volumes of {K}ähler-{E}instein {F}ano manifolds}, - JOURNAL = {Amer. J. Math.}, - FJOURNAL = {American Journal of Mathematics}, - VOLUME = {140}, - YEAR = {2018}, - NOTE = {\href{https://doi.org/10.1353/ajm.2018.0009}{DOI:10.1353/ajm.2018.0009}}, - NUMBER = {2}, - PAGES = {391--414}, - ISSN = {0002-9327}, - MRCLASS = {32Q25 (14J45 53C25 53C55)}, - MRNUMBER = {3783213}, -MRREVIEWER = {Cristiano Spotti}, - DOI = {10.1353/ajm.2018.0009}, - URL = {https://doi.org/10.1353/ajm.2018.0009}, -} - -@article {MR3797604, - AUTHOR = {Liu, Yuchen}, - TITLE = {The volume of singular {K}ähler-{E}instein {F}ano varieties}, - JOURNAL = {Compos. Math.}, - FJOURNAL = {Compositio Mathematica}, - VOLUME = {154}, - YEAR = {2018}, - NOTE = {\href{https://doi.org/10.1112/S0010437X18007042}{DOI:10.1112/S0010437X18007042}}, - NUMBER = {6}, - PAGES = {1131--1158}, - ISSN = {0010-437X}, - MRCLASS = {14J45 (14B05 14L24 32Q15)}, - MRNUMBER = {3797604}, -MRREVIEWER = {Giulio Codogni}, - DOI = {10.1112/S0010437X18007042}, - URL = {https://doi.org/10.1112/S0010437X18007042}, -} - -@incollection {MR3821147, - AUTHOR = {Cantat, Serge}, - TITLE = {The {C}remona group}, - BOOKTITLE = {Algebraic geometry: {S}alt {L}ake {C}ity 2015}, - SERIES = {Proc. Sympos. Pure Math.}, - VOLUME = {97}, - PAGES = {101--142}, - PUBLISHER = {Amer. Math. 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Preprint \href{https://arxiv.org/abs/1508.02456}{arXiv:1508.02456}.}, - VOLUME = {129}, - YEAR = {2019}, - PAGES = {1--49}, - ISSN = {0073-8301}, - MRCLASS = {14E30 (32S65)}, - MRNUMBER = {3949026}, - DOI = {10.1007/s10240-019-00105-w}, - URL = {https://doi.org/10.1007/s10240-019-00105-w}, -} - -@article {MR3953506, - AUTHOR = {Höring, Andreas and Peternell, Thomas}, - TITLE = {Algebraic integrability of foliations with numerically trivial - canonical bundle}, - JOURNAL = {Invent. Math.}, - FJOURNAL = {Inventiones Mathematicae}, - VOLUME = {216}, - YEAR = {2019}, - NOTE = {\href{https://doi.org/10.1007/s00222-018-00853-2}{DOI:10.1007/s00222-018-00853-2}. 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Vitter, III}, - DOI = {10.2969/jmsj/03220325}, - URL = {https://doi.org/10.2969/jmsj/03220325}, -} - - -@article {MR577360, - AUTHOR = {Siu, Yum-Tong and Yau, Shing-Tung}, - TITLE = {Compact {K}ähler manifolds of positive bisectional curvature}, - JOURNAL = {Invent. Math.}, - FJOURNAL = {Inventiones Mathematicae}, - VOLUME = 59, - YEAR = 1980, - NUMBER = 2, - PAGES = {189--204}, - ISSN = {0020-9910}, - CODEN = {INVMBH}, - MRCLASS = {58E20 (53C55)}, - MRNUMBER = 577360, - MRREVIEWER = {John C. Wood}, - DOI = {10.1007/BF01390043}, - URL = {https://doi.org/10.1007/BF01390043}, -} - -@book {MR580152, - AUTHOR = {Grauert, Hans and Remmert, Reinhold}, - TITLE = {Theory of {S}tein spaces}, - SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]}, - VOLUME = {236}, - NOTE = {Translated from the German by Alan Huckleberry. \href{https://10.1007/978-1-4757-4357-9}{DOI:10.1007/978-1-4757-4357-9}}, - PUBLISHER = {Springer-Verlag, Berlin-New York}, - YEAR = {1979}, - PAGES = {xxi+249}, - ISBN = {3-540-90388-7}, - MRCLASS = {32-01}, - MRNUMBER = {580152}, -} - -@article{MR582515, - Author = {Greuel, Gert-Martin}, - Coden = {MAANA3}, - Doi = {10.1007/BF01364456}, - Fjournal = {Mathematische Annalen}, - Issn = {0025-5831}, - Journal = {Math. Ann.}, - Mrclass = {32B30 (14B07)}, - Mrnumber = {582515 (82e:32009)}, - Mrreviewer = {Jonathan M. Wahl}, - Number = 2, - Pages = {157--173}, - Title = {Dualität in der lokalen {K}ohomologie isolierter - {S}ingularitäten}, - Url = - {https://doi.org.offcampus.lib.washington.edu/10.1007/BF01364456}, - Volume = 250, - Year = 1980, - Bdsk-Url-1 = - {https://doi.org.offcampus.lib.washington.edu/10.1007/BF01364456}, - Bdsk-Url-2 = {https://doi.org/10.1007/BF01364456} -} - - -@article {MR584075, - AUTHOR = {Siu, Yum-Tong}, - TITLE = {The complex-analyticity of harmonic maps and the strong rigidity of compact {K}ähler manifolds}, - JOURNAL = {Ann. of Math. (2)}, - FJOURNAL = {Annals of Mathematics. Second Series}, - VOLUME = {112}, - YEAR = {1980}, - NUMBER = {1}, - PAGES = {73--111}, - ISSN = {0003-486X}, - MRCLASS = {53C55 (32H99 58E20)}, - MRNUMBER = {584075}, -MRREVIEWER = {M. Kalka}, - DOI = {10.2307/1971321}, - URL = {https://doi.org/10.2307/1971321}, -} - -@article{MR597077, - Author = {Hartshorne, Robin}, - Coden = {MAANA3}, - Fjournal = {Mathematische Annalen}, - Issn = {0025-5831}, - Journal = {Math. Ann.}, - Mrclass = {14F05 (14D22)}, - Mrnumber = {597077 (82b:14011)}, - Mrreviewer = {Klaus Hulek}, - Number = 2, - Pages = {121--176}, - Title = {Stable reflexive sheaves}, - Note = {\href{https://doi.org/10.1007/BF01467074}{DOI:10.1007/BF01467074}}, - Volume = 254, - Year = 1980 -} - -@article {MR622451, - AUTHOR = {Kawamata, Yujiro}, - TITLE = {Characterization of abelian varieties}, - JOURNAL = {Compositio Math.}, - FJOURNAL = {Compositio Mathematica}, - VOLUME = {43}, - YEAR = {1981}, - NUMBER = {2}, - NOTE = {\href{http://www.numdam.org/item?id=CM_1981__43_2_253_0}{numdam.CM-1981-43-2-253-0}}, - PAGES = {253--276}, - ISSN = {0010-437X}, - MRCLASS = {14J10 (32J15)}, - MRNUMBER = {622451}, -MRREVIEWER = {Daniel Comenetz}, - URL = {http://www.numdam.org/item?id=CM_1981__43_2_253_0}, -} - -@article{MR635391, - Author = {Kobayashi, Shoshichi}, - Coden = {JDMVA7}, - Fjournal = {Jahresbericht der Deutschen Mathematiker-Vereinigung}, - Issn = {0012-0456}, - Journal = {Jahresber. Deutsch. Math.-Verein.}, - Mrclass = {32C10 (53C55)}, - Mrnumber = {635391 (82m:32008)}, - Mrreviewer = {Marcus Wright}, - Number = 4, - Pages = {147--158}, - Title = {Recent results in complex differential geometry}, - Volume = 83, - Year = 1981 -} - -@article {MR641815, - AUTHOR = {Viehweg, Eckart}, - TITLE = {Die {A}dditivität der {K}odaira {D}imension für projektive {F}aserräume über {V}arietäten des allgemeinen {T}yps}, - JOURNAL = {J. Reine Angew. Math.}, - FJOURNAL = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]}, - VOLUME = {330}, - YEAR = {1982}, - PAGES = {132--142}, - ISSN = {0075-4102}, - MRCLASS = {14D05 (14F05 14J10)}, - MRNUMBER = {641815}, -MRREVIEWER = {Takao Fujita}, - NOTE = {\href{https://doi.org/10.1515/crll.1982.330.132}{DOI:10.1515/crll.1982.330.132}}, - DOI = {10.1515/crll.1982.330.132}, - URL = {https://doi.org/10.1515/crll.1982.330.132}, -} - -@article {MR641971, - AUTHOR = {Mori, Shigefumi and Mukai, Shigeru}, - TITLE = {Classification of {F}ano {$3$}-folds with {$B_{2}\geq 2$}}, - JOURNAL = {Manuscripta Math.}, - FJOURNAL = {Manuscripta Mathematica}, - VOLUME = 36, - YEAR = {1981/82}, - NUMBER = 2, - NOTE = {\href{https://doi.org/10.1007/BF01170131}{DOI:10.1007/BF01170131}}, - PAGES = {147--162}, - ISSN = {0025-2611}, - CODEN = {MSMHB2}, - MRCLASS = {14J30 (14J10)}, - MRNUMBER = 641971, - MRREVIEWER = {Mary Schaps}, - DOI = {10.1007/BF01170131}, - URL = {https://doi.org/10.1007/BF01170131}, -} - -@article {MR670921, - AUTHOR = {Ancona, Vincenzo}, - TITLE = {Faisceaux amples sur les espaces analytiques}, - JOURNAL = {Trans. Amer. Math. Soc.}, - FJOURNAL = {Transactions of the American Mathematical Society}, - VOLUME = 274, - YEAR = 1982, - NOTE = {\href{https://doi.org/10.2307/1999498}{DOI:10.2307/1999498}}, - NUMBER = 1, - PAGES = {89--100}, - ISSN = {0002-9947}, - MRCLASS = {32L10 (32C35 32J20)}, - MRNUMBER = 670921, - MRREVIEWER = {M. Schneider}, - DOI = {10.2307/1999498}, - URL = {https://doi.org/10.2307/1999498}, -} - -@book {MR673560, - AUTHOR = {Ancona, Vincenzo and Tomassini, Giuseppe}, - TITLE = {Modifications analytiques}, - SERIES = {Lecture Notes in Mathematics}, - VOLUME = 943, - PUBLISHER = {Springer-Verlag, Berlin-New York}, - YEAR = 1982, - PAGES = {iv+120}, - NOTE = - {\href{https://doi.org/10.1007/BFb0095882}{DOI:10.1007/BFb0095882}}, - ISBN = {3-540-11570-6}, - MRCLASS = {32C45 (14E15)}, - MRNUMBER = {673560 (84g:32022)}, - MRREVIEWER = {H. Kerner}, -} - -@book {MR676809, - AUTHOR = {Friedlander, Eric M.}, - TITLE = {Étale homotopy of simplicial schemes}, - SERIES = {Annals of Mathematics Studies}, - VOLUME = 104, - PUBLISHER = {Princeton University Press, Princeton, N.J.; University of - Tokyo Press, Tokyo}, - YEAR = 1982, - PAGES = {vii+190}, - ISBN = {0-691-08288-X; 0-691-08317-7}, - MRCLASS = {55P99 (14F35 55-02)}, - MRNUMBER = 676809, - MRREVIEWER = {V. P. Snaith}, -} - -@article{MR707162, - Author = {Friedman, Robert}, - Coden = {ANMAAH}, - Doi = {10.2307/2006955}, - Fjournal = {Annals of Mathematics. Second Series}, - Issn = {0003-486X}, - Journal = {Ann. of Math. (2)}, - Mrclass = {32G11 (14D20 14J28 32G13)}, - Mrnumber = {707162 (85g:32029)}, - Mrreviewer = {David R. Morrison}, - Number = 1, - Pages = {75--114}, - Title = {Global smoothings of varieties with normal crossings}, - Url = {https://doi.org/10.2307/2006955}, - Volume = 118, - Year = 1983, - Bdsk-Url-1 = {https://doi.org/10.2307/2006955} -} - -@incollection {MR715648, - AUTHOR = {Mori, Shigefumi and Mukai, Shigeru}, - TITLE = {On {F}ano {$3$}-folds with {$B_{2}\geq 2$}}, - BOOKTITLE = {Algebraic varieties and analytic varieties ({T}okyo, 1981)}, - SERIES = {Adv. Stud. Pure Math.}, - VOLUME = {1}, - PAGES = {101--129}, - PUBLISHER = {North-Holland, Amsterdam}, - YEAR = {1983}, - MRCLASS = {14J30}, - MRNUMBER = {715648}, -MRREVIEWER = {I. Dolgachev}, - NOTE = {\href{https://doi.org/10.2969/aspm/00110101}{DOI:10.2969/aspm/00110101}}, - DOI = {10.2969/aspm/00110101}, - URL = {https://doi.org/10.2969/aspm/00110101}, -} - -@incollection{MR717614, - Author = {Mumford, David}, - Booktitle = {Arithmetic and geometry, {V}ol. {II}}, - Mrclass = {14H10 (14C15)}, - Mrnumber = {717614 (85j:14046)}, - Mrreviewer = {Werner Kleinert}, - Note = {\href{https://doi.org/10.1007/978-1-4757-9286-7_12}{DOI: - 10.1007/987-1-4757-9286-7\-12}}, - Pages = {271--328}, - Publisher = {Birkhäuser Boston, Boston, MA}, - Series = {Progr. Math.}, - Title = {Towards an enumerative geometry of the moduli space of curves}, - Volume = 36, - Year = 1983 -} - -@article {MR723219, - AUTHOR = {Levine, Marc}, - TITLE = {Pluri-canonical divisors on {K}ähler manifolds}, - JOURNAL = {Invent. Math.}, - FJOURNAL = {Inventiones Mathematicae}, - VOLUME = 74, - YEAR = 1983, - NUMBER = 2, - PAGES = {293--303}, - ISSN = {0020-9910}, - MRCLASS = {32J25 (14J15)}, - MRNUMBER = 723219, - MRREVIEWER = {D. Lieberman}, - DOI = {10.1007/BF01394318}, - URL = {https://doi.org/10.1007/BF01394318}, -} - -@incollection {MR728609, - AUTHOR = {Fujiki, Akira}, - TITLE = {On primitively symplectic compact {K}\"{a}hler {$V$}-manifolds of - dimension four}, - BOOKTITLE = {Classification of algebraic and analytic manifolds ({K}atata, - 1982)}, - SERIES = {Progr. Math.}, - VOLUME = {39}, - PAGES = {71--250}, - PUBLISHER = {Birkh\"{a}user Boston, Boston, MA}, - YEAR = {1983}, - MRCLASS = {32G05 (32J99)}, - MRNUMBER = {728609}, -MRREVIEWER = {Daniel Barlet}, -} - -@article {MR765916, - AUTHOR = {Andreatta, Marco and Silva, Alessandro}, - TITLE = {On weakly rational singularities in complex analytic geometry}, - JOURNAL = {Ann. Mat. Pura Appl. (4)}, - FJOURNAL = {Annali di Matematica Pura ed Applicata. Serie Quarta}, - VOLUME = 136, - YEAR = 1984, - PAGES = {65--76}, - ISSN = {0003-4622}, - MRCLASS = {32C40 (14B05 32B30)}, - MRNUMBER = 765916, - MRREVIEWER = {Bernd Herzog}, - NOTE = - {\href{https://doi.org/10.1007/BF01773377}{DOI:10.1007/BF01773377}.}, - DOI = {10.1007/BF01773377}, - URL = {https://doi.org/10.1007/BF01773377}, -} - -@inproceedings{MR772058, - Author = {Gillet, Henri}, - Booktitle = {Proceedings of the {L}uminy conference on algebraic - {$K$}-theory ({L}uminy, 1983)}, - Coden = {JPAAA2}, - Doi = {10.1016/0022-4049(84)90036-7}, - Fjournal = {Journal of Pure and Applied Algebra}, - Issn = {0022-4049}, - Journal = {J. Pure Appl. Algebra}, - Mrclass = {14C35 (14C17 18F25 19E20)}, - Mrnumber = {772058 (86b:14006)}, - Mrreviewer = {Daniel R. Grayson}, - Number = {2-3}, - Pages = {193--240}, - Title = {Intersection theory on algebraic stacks and {$Q$}-varieties}, - Url = {https://doi.org/10.1016/0022-4049(84)90036-7}, - Volume = 34, - Year = 1984, - Bdsk-Url-1 = {https://doi.org/10.1016/0022-4049(84)90036-7} -} - -@article {MR780664, - AUTHOR = {Noguchi, Junjiro}, - TITLE = {On the value distribution of meromorphic mappings of covering spaces over {${\bf C}^m$} into algebraic varieties}, - JOURNAL = {J. Math. Soc. Japan}, - FJOURNAL = {Journal of the Mathematical Society of Japan}, - VOLUME = {37}, - YEAR = {1985}, - NOTE = {\href{https://doi.org/10.2969/jmsj/03720295}{DOI:10.2969/jmsj/03720295}}, - NUMBER = {2}, - PAGES = {295--313}, - ISSN = {0025-5645}, - MRCLASS = {32H30}, - MRNUMBER = {780664}, -MRREVIEWER = {Alexander A. Pankov}, - DOI = {10.2969/jmsj/03720295}, - URL = {https://doi.org/10.2969/jmsj/03720295}, -} - -@book {MR781344, - AUTHOR = {Bröcker, Theodor and tom Dieck, Tammo}, - TITLE = {Representations of compact {L}ie groups}, - SERIES = {Graduate Texts in Mathematics}, - VOLUME = 98, - PUBLISHER = {Springer-Verlag, New York}, - YEAR = 1985, - PAGES = {x+313}, - ISBN = {0-387-13678-9}, - MRCLASS = {22E45 (57-01)}, - MRNUMBER = 781344, - MRREVIEWER = {R. Schultz}, - NOTE = {\href{https://doi.org/10.1007/978-3-662-12918-0}{DOI:10.1007/978-3-662-12918-0}.}, - DOI = {10.1007/978-3-662-12918-0}, - URL = {https://doi.org/10.1007/978-3-662-12918-0}, -} - -@article{MR782236, - Author = {Kawamata, Yujiro}, - Coden = {INVMBH}, - Doi = {10.1007/BF01388524}, - Fjournal = {Inventiones Mathematicae}, - Issn = {0020-9910}, - Journal = {Invent. Math.}, - Mrclass = {14C20 (14J10)}, - Mrnumber = {782236 (87h:14005)}, - Mrreviewer = {Rick Miranda}, - Number = 3, - NOTE = {\href{https://doi.org/10.1007/BF01388524}{DOI:10.1007/BF01388524}}, - Pages = {567--588}, - Title = {Pluricanonical systems on minimal algebraic varieties}, - Url = {https://doi.org/10.1007/BF01388524}, - Volume = 79, - Year = 1985, - Bdsk-Url-1 = {https://doi.org/10.1007/BF01388524} -} - -@book{MR782881, - Address = {Nancy}, - Author = {Huckleberry, Alan and Oeljeklaus, Eberhard}, - Isbn = {2-903594-07-4}, - Mrclass = {32M10}, - Mrnumber = {782881 (86g:32050)}, - Mrreviewer = {D. N. Akhiezer}, - Pages = {iv+178+xiv}, - Publisher = {Université de Nancy Institut Élie Cartan}, - Series = {Institut Élie Cartan}, - Title = {Classification theorems for almost homogeneous spaces}, - Volume = 9, - Year = 1984 -} - -@article {MR791292, - AUTHOR = {Levine, Marc}, - TITLE = {Pluri-canonical divisors on {K}ähler manifolds. {II}}, - JOURNAL = {Duke Math. J.}, - FJOURNAL = {Duke Mathematical Journal}, - VOLUME = 52, - YEAR = 1985, - NUMBER = 1, - PAGES = {61--65}, - ISSN = {0012-7094}, - MRCLASS = {32J25}, - MRNUMBER = 791292, - MRREVIEWER = {D. Lieberman}, - DOI = {10.1215/S0012-7094-85-05205-6}, - URL = {https://doi.org/10.1215/S0012-7094-85-05205-6}, -} - -@article{MR818915, - Author = {Lubotzky, Alexander and Magid, Andy R.}, - Coden = {MAMCAU}, - Doi = {10.1090/memo/0336}, - Fjournal = {Memoirs of the American Mathematical Society}, - Issn = {0065-9266}, - Journal = {Mem. Amer. Math. Soc.}, - Mrclass = {20C15 (14D20)}, - Mrnumber = {818915 (87c:20021)}, - Mrreviewer = {Avner Ash}, - Number = 336, - Pages = {xi+117}, - Title = {Varieties of representations of finitely generated groups}, - Url = {https://doi.org/10.1090/memo/0336}, - Volume = 58, - Year = 1985, - Bdsk-Url-1 = {https://doi.org/10.1090/memo/0336} -} - -@article{MR82, - Author = {Mehta, Vikram B. and Ramanathan, Annamalai}, - Coden = {MAANA3}, - Fjournal = {Mathematische Annalen}, - Issn = {0025-5831}, - Journal = {Math. Ann.}, - Mrclass = {14F05}, - Mrnumber = {83f:14013}, - Mrreviewer = {Klaus Hulek}, - Number = 3, - Pages = {213--224}, - Title = {Semistable sheaves on projective varieties and their - restriction to curves}, - Volume = 258, - Year = {1981/82} -} - -@incollection {MR825744, - AUTHOR = {Ancona, Vincenzo and Silva, Alessandro}, - TITLE = {Numerically effective bundles on {M}oi\v{s}ezon and strongly pseudoconvex manifolds}, - BOOKTITLE = {Seminar on deformations (\Lódź/{W}arsaw, 1982/84)}, - SERIES = {Lecture Notes in Math.}, - VOLUME = {1165}, - PAGES = {1--13}, - PUBLISHER = {Springer, Berlin}, - YEAR = {1985}, - MRCLASS = {32L20}, - MRNUMBER = {825744}, -MRREVIEWER = {Thomas Peternell}, - NOTE = {\href{https://doi.org/10.1007/BFb0076142}{DOI:10.1007/BFb0076142}}, - DOI = {10.1007/BFb0076142}, - URL = {https://doi.org/10.1007/BFb0076142}, -} - -@article {MR83045, - AUTHOR = {Stein, Karl}, - TITLE = {Analytische {Z}erlegungen komplexer {R}\"{a}ume}, - JOURNAL = {Math. Ann.}, - FJOURNAL = {Mathematische Annalen}, - VOLUME = {132}, - YEAR = {1956}, - PAGES = {63--93}, - ISSN = {0025-5831}, - MRCLASS = {30.0X}, - MRNUMBER = {83045}, -MRREVIEWER = {Heinrich Behnke}, - DOI = {10.1007/BF01343331}, - URL = {https://doi.org/10.1007/BF01343331}, -} - -@article{MR84, - Author = {Mehta, Vikram B. and Ramanathan, Annamalai}, - Coden = {INVMBH}, - Doi = {10.1007/BF01389140}, - Fjournal = {Inventiones Mathematicae}, - Issn = {0020-9910}, - Journal = {Invent. Math.}, - Mrclass = {14F05}, - Mrnumber = {751136 (85m:14026)}, - Mrreviewer = {P. E. Newstead}, - Number = 1, - Pages = {163--172}, - Title = {Restriction of stable sheaves and representations of the - fundamental group}, - Note = {\href{https://doi.org/10.1007/BF01389140}{DOI: - 10.1007/BF01389140}}, - Url = {https://doi.org/10.1007/BF01389140}, - Volume = 77, - Year = 1984, - Bdsk-Url-1 = {https://doi.org/10.1007/BF01389140} -} - -@article{MR853449, - Author = {Esnault, Hélène and Viehweg, Eckart}, - Coden = {INVMBH}, - Fjournal = {Inventiones Mathematicae}, - Issn = {0020-9910}, - Journal = {Invent. Math.}, - Mrclass = {32L20 (14F40)}, - Mrnumber = {853449 (87j:32088)}, - Mrreviewer = {Siegmund Kosarew}, - Number = 1, - Pages = {161--194}, - Title = {Logarithmic de {R}ham complexes and vanishing theorems}, - Volume = 86, - Year = 1986 -} - -@book {MR867684, - AUTHOR = {Besse, Arthur L.}, - TITLE = {Einstein manifolds}, - SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results - in Mathematics and Related Areas (3)]}, - VOLUME = 10, - PUBLISHER = {Springer-Verlag, Berlin}, - YEAR = 1987, - PAGES = {xii+510}, - ISBN = {3-540-15279-2}, - MRCLASS = {53C25 (53-02 53C21 53C30 53C55 58D17 58E11)}, - MRNUMBER = {867684 (88f:53087)}, - MRREVIEWER = {S. M. Salamon}, - DOI = {10.1007/978-3-540-74311-8}, - URL = {https://doi.org/10.1007/978-3-540-74311-8}, - NOTE = - {\href{https://doi.org/10.1007/978-3-540-74311-8}{DOI:10.1007/978-3-540-74311-8}} -} - -@article {MR888704, - AUTHOR = {Seitz, Gary M.}, - TITLE = {The maximal subgroups of classical algebraic groups}, - JOURNAL = {Mem. Amer. Math. Soc.}, - FJOURNAL = {Memoirs of the American Mathematical Society}, - VOLUME = 67, - YEAR = 1987, - NUMBER = 365, - PAGES = {iv+286}, - ISSN = {0065-9266}, - CODEN = {MAMCAU}, - MRCLASS = {20G15 (20E28 20G05)}, - MRNUMBER = 888704, - MRREVIEWER = {James E. Humphreys}, - DOI = {10.1090/memo/0365}, - URL = {https://doi.org/10.1090/memo/0365}, -} - -@book {MR921027, - AUTHOR = {Arnol$'$d, Vladimir I.}, - TITLE = {Geometrische {M}ethoden in der {T}heorie der gewöhnlichen {D}ifferentialgleichungen}, - NOTE = {Translated from the Russian by Ernst Günter Giessmann, Bernd Graw and Horst Theel. \href{https://doi.org/10.1007/978-3-0348-7125-9}{DOI:10.1007/978-3-0348-7125-9}}, - PUBLISHER = {Birkhäuser Verlag, Basel}, - YEAR = {1987}, - PAGES = {320}, - ISBN = {3-7643-1879-1}, - MRCLASS = {58Fxx (34-02 34Cxx)}, - MRNUMBER = {921027}, - DOI = {10.1007/978-3-0348-7125-9}, - URL = {https://doi.org/10.1007/978-3-0348-7125-9}, -} - -@article {MR92195, - AUTHOR = {Hirzebruch, Friedrich and Kodaira, Kunihiko}, - TITLE = {On the complex projective spaces}, - JOURNAL = {J. Math. Pures Appl. (9)}, - FJOURNAL = {Journal de Mathématiques Pures et Appliquées. Neuvi\`eme Série}, - VOLUME = {36}, - YEAR = {1957}, - PAGES = {201--216}, - ISSN = {0021-7824}, - MRCLASS = {53.3X}, - MRNUMBER = {92195}, -MRREVIEWER = {E. Vesentini}, -} - -@article {MR925989, - AUTHOR = {Alperin, Roger C.}, - TITLE = {An elementary account of {S}elberg's lemma}, - JOURNAL = {Enseign. Math. (2)}, - FJOURNAL = {L'Enseignement Mathématique. Revue Internationale. 2e Série}, - VOLUME = {33}, - YEAR = {1987}, - NOTE = {\href{https://doi.org/10.5169/seals-87896}{DOI:10.5169/seals-87896}}, - NUMBER = {3-4}, - PAGES = {269--273}, - ISSN = {0013-8584}, - MRCLASS = {20H20}, - MRNUMBER = {925989}, -MRREVIEWER = {A. E. Zalesski\u{\i}}, -} - -@article {MR932782, - AUTHOR = {Ancona, Vincenzo}, - TITLE = {Vanishing and nonvanishing theorems for numerically effective line bundles on complex spaces}, - JOURNAL = {Ann. Mat. Pura Appl. (4)}, - FJOURNAL = {Annali di Matematica Pura ed Applicata. Serie Quarta}, - VOLUME = {149}, - YEAR = {1987}, - PAGES = {153--164}, - ISSN = {0003-4622}, - MRCLASS = {32L20 (14E30 14J10)}, - MRNUMBER = {932782}, -MRREVIEWER = {Yujiro Kawamata}, - NOTE = {\href{https://doi.org/10.1007/BF01773931}{DOI:10.1007/BF01773931}}, - DOI = {10.1007/BF01773931}, - URL = {https://doi.org/10.1007/BF01773931}, -} - -@book{MR941969, - Address = {Stuttgart}, - Author = {Stöcker, Ralph and Zieschang, Heiner}, - Isbn = {3-519-02226-5}, - Mrclass = {55-01}, - Mrnumber = {941969 (89e:55001)}, - Mrreviewer = {Hans-Werner Henn}, - Note = {Eine Einführung. [An introduction]}, - Pages = {x+414}, - Publisher = {B. G. Teubner}, - Series = {Mathematische Leitfäden. [Mathematical Textbooks]}, - Title = {Algebraische {T}opologie}, - Year = 1988 -} - -@article {MR944576, - AUTHOR = {Kollár, János}, - TITLE = {Sharp effective {N}ullstellensatz}, - JOURNAL = {J. Amer. Math. Soc.}, - FJOURNAL = {Journal of the American Mathematical Society}, - VOLUME = {1}, - YEAR = {1988}, - NUMBER = {4}, - NOTE = {\href{https://doi.org/10.2307/1990996}{DOI:10.2307/1990996}}, - PAGES = {963--975}, - ISSN = {0894-0347}, - MRCLASS = {12E99 (11C08 11J99 13B25)}, - MRNUMBER = {944576}, -MRREVIEWER = {D. W. Masser}, - DOI = {10.2307/1990996}, - URL = {https://doi.org/10.2307/1990996}, -} - -@article{MR944577, - Author = {Simpson, Carlos T.}, - Doi = {10.2307/1990994}, - Fjournal = {Journal of the American Mathematical Society}, - Issn = {0894-0347}, - Journal = {J. Amer. Math. Soc.}, - Mrclass = {58E15 (32L15 53C25 53C55)}, - Mrnumber = {944577 (90e:58026)}, - Note = {\href{https://doi.org/10.1090/S0894-0347-1988-0944577-9}{DOI:10.1090/S0894-0347-1988-0944577-9}}, - Number = 4, - Pages = {867--918}, - Title = {Constructing variations of {H}odge structure using {Y}ang-{M}ills theory and applications to uniformization}, - Url = {https://doi.org/10.2307/1990994}, - Volume = 1, - Year = 1988, - Bdsk-Url-1 = {https://doi.org/10.2307/1990994} -} - -@incollection{MR946238, - Address = {Amsterdam}, - Author = {Fujita, Takao}, - Booktitle = {Algebraic geometry, {S}endai, 1985}, - Mrclass = {14C20 (14J40)}, - Mrnumber = {946238 (89d:14006)}, - Mrreviewer = {Antonio Lanteri}, - Pages = {167--178}, - Publisher = {North-Holland}, - Series = {Adv. Stud. Pure Math.}, - Title = {On polarized manifolds whose adjoint bundles are not semipositive}, - Volume = 10, - Year = 1987, - Note = {\href{https://doi.org/10.2969/aspm/01010167}{DOI:10.2969/aspm/01010167}} -} - -@incollection {MR946250, - AUTHOR = {Nakayama, Noboru}, - TITLE = {The lower semicontinuity of the plurigenera of complex varieties}, - BOOKTITLE = {Algebraic geometry, {S}endai, 1985}, - SERIES = {Adv. Stud. Pure Math.}, - VOLUME = 10, - PAGES = {551--590}, - PUBLISHER = {North-Holland, Amsterdam}, - YEAR = 1987, - MRCLASS = {14J15 (14E30 32J15)}, - MRNUMBER = {946250 (89h:14028)}, - MRREVIEWER = {David R. Morrison}, - NOTE = {\href{https://doi.org/10.2969/aspm/01010551}{DOI:10.2969/aspm/01010551}}, -} - -@book{MR947141, - Address = {New York}, - Author = {Arnol$'$d, Vladimir I.}, - Edition = {Second}, - Isbn = {0-387-96649-8}, - Mrclass = {58Fxx (34Cxx 70H05 70K30 70K99)}, - Mrnumber = {947141 (89h:58049)}, - Note = {Translated from the Russian by Joseph Szücs [J{{\'o}}zsef M. Sz{\H{u}}cs]}, - Pages = {xiv+351}, - Publisher = {Springer-Verlag}, - Series = {Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]}, - Title = {Geometrical methods in the theory of ordinary differential equations}, - Volume = 250, - Year = 1988 -} - -@article {MR973802, - AUTHOR = {Varouchas, Jean}, - TITLE = {Kähler spaces and proper open morphisms}, - JOURNAL = {Math. Ann.}, - FJOURNAL = {Mathematische Annalen}, - VOLUME = 283, - YEAR = 1989, - NUMBER = 1, - NOTE = - {\href{https://doi.org/10.1007/BF01457500}{DOI:10.1007/BF01457500}}, - PAGES = {13--52}, - ISSN = {0025-5831}, - CODEN = {MAANA}, - MRCLASS = {32C15 (32F05 32G10 32H35)}, - MRNUMBER = 973802, - MRREVIEWER = {Siegmund Kosarew}, - DOI = {10.1007/BF01457500}, - URL = {https://doi.org/10.1007/BF01457500}, -} - -@book {MR982494, - AUTHOR = {Reid, Miles}, - TITLE = {Undergraduate algebraic geometry}, - SERIES = {London Mathematical Society Student Texts}, - NOTE = {\href{https://doi.org/10.1017/CBO9781139163699}{DOI:10.1017/CBO9781139163699}}, - VOLUME = {12}, - PUBLISHER = {Cambridge University Press, Cambridge}, - YEAR = {1988}, - PAGES = {viii+129}, - ISBN = {0-521-35559-1; 0-521-35662-8}, - MRCLASS = {14-01 (00A05)}, - MRNUMBER = {982494}, -MRREVIEWER = {Marko Roczen}, - DOI = {10.1017/CBO9781139163699}, - URL = {https://doi.org/10.1017/CBO9781139163699}, -} - -@inproceedings{MU83, - Author = {S. Mukai and H. Umemura}, - Booktitle = {Algebraic geometry, Proc. Jap.-Fr. Conf., Tokyo and Kyoto - 1982}, - Editor = {M. Raynaud and T. Shioda}, - Pages = {490-518}, - Publisher = {Springer}, - Series = {Lect. Notes Math}, - Title = {{Minimal Rational Threefolds}}, - Volume = 1016, - Year = 1983 -} - -@article {MZ18, - AUTHOR = {Meng, Sheng and Zhang, De-Qi}, - TITLE = {Jordan property for non-linear algebraic groups and projective varieties}, - JOURNAL = {Amer. J. Math.}, - FJOURNAL = {American Journal of Mathematics}, - VOLUME = 140, - YEAR = 2018, - NOTE = {\href{https://doi.org/10.1353/ajm.2018.0026}{DOI:10.1353/ajm.2018.0026}. Preprint \href{https://arxiv.org/abs/1507.02230}{arXiv:math/1507.02230}}, - NUMBER = 2, - PAGES = {403--418}, - ISSN = {0002-9327}, - MRCLASS = {14E07}, - MRNUMBER = 3483470, - MRREVIEWER = {Zinovy Reichstein}, - DOI = {10.1353/ajm.2016.0017}, - URL = {https://doi.org/10.1353/ajm.2016.0017}, -} - -@book{Ma91, - Author = {W.S. 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Hartshorne}, - Note = {Correction: {\it Amer.\ J.\ Math.\/}, 91:851, 1969}, - Pages = {668--684}, - Title = {Two fundamental theorems on deformations of polarized - varieties}, - Volume = 86, - Year = 1964 -} - -@article{Mat-Mum64corr, - Author = {Matsusaka, T. and Mumford, D.}, - Journal = {Amer. J. Math.}, - Mrclass = {14.51}, - Mrnumber = {40 \#1398}, - Pages = 851, - Title = {Correction to: ``{T}wo fundamental theorems on deformations of - polarized varieties''}, - Volume = 91, - Year = 1969 -} - -@book{Mat89, - Author = {H.~Matsumura}, - Number = 8, - Publisher = {Cambridge University Press}, - Series = {Cambridge studies in advanced mathematics}, - Title = {Commutitative ring theory}, - Year = 1989 -} - -@book{Matsuki02, - Address = {New York}, - Author = {Matsuki, Kenji}, - Isbn = {0-387-98465-8}, - Mrclass = {14E30 (14-02 14E05 14J17 14J30)}, - Mrnumber = {2002m:14011}, - Mrreviewer = {Massimiliano Mella}, - Pages = {xxiv+478}, - Publisher = {Springer-Verlag}, - Series = {Universitext}, - Title = {Introduction to the {M}ori program}, - Year = 2002 -} - -@book{McDS95, - Address = {New York}, - Author = {McDuff, Dusa and Salamon, Dietmar}, - Isbn = {0-19-851177-9}, - Mrclass = {58F05 (53C15 57R57 58E05)}, - Mrnumber = {1373431 (97b:58062)}, - Mrreviewer = {Hansjörg Geiges}, - Note = {Oxford Science Publications}, - Pages = {viii+425}, - Publisher = {The Clarendon Press Oxford University Press}, - Series = {Oxford Mathematical Monographs}, - Title = {Introduction to symplectic topology}, - Year = 1995 -} - -@book{McL75, - Address = {Berlin}, - Author = {Mac Lane, Saunders}, - Isbn = {3-540-58662-8}, - Mrclass = {18-02 (18Axx 18Cxx 18Gxx)}, - Mrnumber = {1344215 (96d:18001)}, - NOTE = {\href{https://doi.org/10.1007/978-3-642-62029-4}{DOI:10.1007/978-3-642-62029-4}. Reprint of the 1975 edition}, - Pages = {x+422}, - Publisher = {Springer-Verlag}, - Series = {Classics in Mathematics}, - Title = {Homology}, - Year = 1995 -} - -@article {Meg97, - AUTHOR = {Megyesi, Gabor}, - TITLE = {Generalisation of the {B}ogomolov-{M}iyaoka-{Y}au inequality - to singular surfaces}, - JOURNAL = {Proc. London Math. Soc. (3)}, - FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, - VOLUME = 78, - YEAR = 1999, - NOTE = {\href{https://doi.org/10.1112/S0024611599001719}{DOI:10.1112/S0024611599001719}}, - NUMBER = 2, - PAGES = {241--282}, - ISSN = {0024-6115}, - MRCLASS = {14J17 (14C17 14J60)}, - MRNUMBER = 1665244, - MRREVIEWER = {Gerhard Pfister}, - DOI = {10.1112/S0024611599001719}, - URL = {https://doi.org/10.1112/S0024611599001719}, -} - -@article{Migliorini95, - Author = {Migliorini, Luca}, - Fjournal = {Journal of Algebraic Geometry}, - Issn = {1056-3911}, - Journal = {J. 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Pure Math.}, - Title = {Deformations of a morphism along a foliation and applications}, - Volume = 46, - Year = 1987 -} - -@misc{Miy92, - Author = {Y.~Miyaoka}, - Note = {misc}, - Title = {Lecture at the university of Utah}, - Year = 1992 -} - -@incollection{Miyanishi-Tsunoda82, - Address = {Boston, MA}, - Author = {Miyanishi, Masayoshi and Tsunoda, Shuichiro}, - Booktitle = {Classification of algebraic and analytic manifolds (Katata, - 1982)}, - Mrclass = {14J10}, - Mrnumber = {728617 (86c:14030)}, - Mrreviewer = {Daniel Comenetz}, - Pages = {499--544}, - Publisher = {Birkhäuser Boston}, - Series = {Progr. Math.}, - Title = {The structure of open algebraic surfaces. {II}}, - Volume = 39, - Year = 1983 -} - -@article{Miyanishi-Tsunoda84, - Author = {Miyanishi, Masayoshi and Tsunoda, Shuichiro}, - Coden = {JJMAAK}, - Fjournal = {Japanese Journal of Mathematics. New Series}, - Issn = {0289-2316}, - Journal = {Japan. J. Math. (N.S.)}, - Mrclass = {14J10 (14J25)}, - Mrnumber = {884420 (88b:14029)}, - Mrreviewer = {L. B{ă}descu}, - Number = 2, - Pages = {195--242}, - Title = {Noncomplete algebraic surfaces with logarithmic {K}odaira - dimension {$-\infty$} and with nonconnected boundaries at - infinity}, - Volume = 10, - Year = 1984 -} - -@inproceedings{Miyanishi82, - Address = {Amsterdam, New York, Oxford}, - Author = {M. Miyanishi}, - Booktitle = {Advanced Studies in Pure Mathematics 1}, - Editor = {S. Iitaka}, - Publisher = {North-Holland publishing company}, - Title = {Algebraic Methods in the Theory of Algebraic Threefolds}, - Year = 1983 -} - -@incollection{Miyaoka87, - Address = {Amsterdam}, - Author = {Miyaoka, Yoichi}, - Booktitle = {Algebraic geometry, Sendai, 1985}, - Mrclass = {14E30 (14F05 14J40)}, - Mrnumber = {89k:14022}, - Mrreviewer = {I. Dolgachev}, - Pages = {449--476}, - Publisher = {North-Holland}, - Series = {Adv. Stud. Pure Math.}, - Title = {The {C}hern classes and {K}odaira dimension of a minimal variety}, - Volume = 10, - Year = 1987, - Note = {\href{https://doi.org/10.2969/aspm/01010449}{DOI:10.2969/aspm/01010449}}, -} - -@article{Mo1, - Author = {G. Mostow}, - Journal = {Am. Math. Soc.}, - Pages = {31--51}, - Title = {Some new decomposition theorems for semi-simple groups}, - Volume = 14, - Year = 1955 -} - -@article{Mo2, - Author = {G. Mostow}, - Journal = {Am. J. Math.}, - Pages = {247--278}, - Title = {On covariant fiberings of Klein spaces}, - Volume = 77, - Year = 1955 -} - -@article{MoSu78, - Author = {Mori, Shigefumi and Sumihiro, Hideyasu}, - Coden = {JMKYAZ}, - Fjournal = {Journal of Mathematics of Kyoto University}, - Issn = {0023-608X}, - Journal = {J. Math. Kyoto Univ.}, - Mrclass = {14J30 (14F10 14J40)}, - Mrnumber = {509496 (80j:14033)}, - Mrreviewer = {P. E. 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Differential Geom.}, - Mrclass = {53C55 (32C10 53C35 58G11)}, - Mrnumber = {89d:53115}, - Mrreviewer = {Hung-Hsi Wu}, - Number = 2, - Pages = {179--214}, - Title = {The uniformization theorem for compact {K}ähler manifolds of - nonnegative holomorphic bisectional curvature}, - Volume = 27, - Year = 1988 -} - -@incollection{Mok94, - Address = {Berlin}, - Author = {Mok, Ngaiming}, - Booktitle = {Geometry from the {P}acific {R}im ({S}ingapore, 1994)}, - Mrclass = {32J27 (32C17)}, - Mrnumber = {1468254 (99a:32038)}, - Mrreviewer = {Philippe P. 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(2)}, - Mrclass = {14J30 (14E35)}, - Mrnumber = {84e:14032}, - Mrreviewer = {Ulf Persson}, - Number = 1, - Pages = {133--176}, - Title = {Threefolds whose canonical bundles are not numerically - effective}, - Volume = 116, - Year = 1982 -} - -@article{Mori85, - Author = {S. Mori}, - Journal = {Nagoya Math. J.}, - Pages = {43--66}, - Title = {{On 3-Dimensional Terminal Singularities}}, - Volume = 98, - Year = 1985 -} - -@incollection{Mori87, - Address = {Providence, RI}, - Author = {Mori, Shigefumi}, - Booktitle = {Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985)}, - Mrclass = {14J10 (14E05 14E30 14J40 14M20)}, - Mrnumber = {927961 (89a:14040)}, - Mrreviewer = {Eckart Viehweg}, - Pages = {269--331}, - Publisher = {Amer. Math. Soc.}, - Series = {Proc. Sympos. 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Studies in Math.}, - Title = {Geometry of {H}ecke cycles. {I}}, - Volume = 8, - Year = 1978 -} - -@book{NSW08, - Address = {Berlin}, - Author = {Neukirch, Jürgen and Schmidt, Alexander and Wingberg, Kay}, - Edition = {Second}, - Isbn = {978-3-540-37888-4}, - Mrclass = {11R34 (11-02 11G45 11R23 11S20 11S25 11S31 12G05)}, - Mrnumber = {2392026 (2008m:11223)}, - Pages = {xvi+825}, - Publisher = {Springer-Verlag}, - Series = {Grundlehren der Mathematischen Wissenschaften [Fundamental - Principles of Mathematical Sciences]}, - Title = {Cohomology of number fields}, - Volume = 323, - Year = 2008 -} - -@article{Nadel91, - Author = {Nadel, Alan M.}, - Fjournal = {Journal of the American Mathematical Society}, - Issn = {0894-0347}, - Journal = {J. Amer. Math. 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To appear in Annals of Maths.}, - Title = {Compactifications of smooth families and of moduli spaces of polarized manifolds}, - Year = 2006 -} - -@incollection{Viehweg83, - Address = {Amsterdam}, - Author = {Viehweg, Eckart}, - Booktitle = {Algebraic varieties and analytic varieties (Tokyo, 1981)}, - Mrclass = {14J10 (14D20 14F05)}, - Mrnumber = {715656 (85b:14041)}, - Mrreviewer = {Yujiro Kawamata}, - Pages = {329--353}, - Publisher = {North-Holland}, - Series = {Adv. Stud. Pure Math.}, - Title = {Weak positivity and the additivity of the {K}odaira dimension - for certain fibre spaces}, - Volume = 1, - Year = 1983 -} - -@book{Viehweg95, - Address = {Berlin}, - Author = {Viehweg, Eckart}, - Isbn = {3-540-59255-5}, - Mrclass = {14-02 (14D20 14D22)}, - Mrnumber = {1368632 (97j:14001)}, - Mrreviewer = {P. E. Newstead}, - NOTE = - {\href{https://doi.org/10.1007/978-3-642-79745-3}{DOI:10.1007/978-3-642-79745-3}}, - Pages = {viii+320}, - Publisher = {Springer-Verlag}, - Series = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results - in Mathematics and Related Areas (3)]}, - Title = {Quasi-projective moduli for polarized manifolds}, - Volume = 30, - Year = 1995 -} - -@article{Viray, - AUTHOR = {Viray, Bianca}, - TITLE = {A family of varieties with exactly one pointless rational fiber}, - JOURNAL = {J. Théor. Nombres Bordeaux}, - FJOURNAL = {Journal de Théorie des Nombres de Bordeaux}, - NOTE = {Available on the internet at \href{http://jtnb.cedram.org/item?id=JTNB_2010__22_3_741_0}{jtnb.cedram.org/item?id=JTNB$\_$2010$\_\_$22$\_$3$\_$741$\_$0}}, - VOLUME = 22, - YEAR = 2010, - NUMBER = 3, - PAGES = {741--745}, - ISSN = {1246-7405}, - MRCLASS = {14G25 (14G05)}, - MRNUMBER = 2769342, - URL = {http://jtnb.cedram.org/item?id=JTNB_2010__22_3_741_0} -} - -@book{Voisin-Hodge1, - Address = {Cambridge}, - Author = {Voisin, Claire}, - Edition = {English}, - Isbn = {978-0-521-71801-1}, - Mrclass = {32J25 (14C30 14D07 32G20)}, - Mrnumber = {2451566 (2009j:32014)}, - Pages = {x+322}, - Publisher = {Cambridge University Press}, - Series = {Cambridge Studies in Advanced Mathematics}, - Title = {Hodge theory and complex algebraic geometry. {I}}, - Volume = 76, - Year = 2007 -} - -@article{Wah83, - Author = {Jonathan Wahl}, - Journal = {Invent. Math.}, - Number = 4, - Pages = {315--322}, - Title = {{A cohomological characterization of $\mathbb P_n$}}, - Note = - {\href{https://doi.org/10.1007/BF01389326}{DOI:10.1007/BF01389326}}, - Volume = 72, - Year = 1983 -} - -@article{Wahl85, - Author = {Wahl, Jonathan M.}, - Coden = {CMPMAF}, - Fjournal = {Compositio Mathematica}, - Issn = {0010-437X}, - Journal = {Compositio Math.}, - Mrclass = {32B30 (14B07 14J17 32G11)}, - Mrnumber = {799816 (87e:32013)}, - Mrreviewer = {Ulrich Karras}, - Number = 3, - Pages = {269--288}, - Title = {A characterization of quasihomogeneous {G}orenstein surface - singularities}, - Volume = 55, - Year = 1985 -} - -@book{Warner83, - Address = {New York}, - Author = {Warner, Frank W.}, - Isbn = {0-387-90894-3}, - Mrclass = {58-01 (22-01 53-01 57R99)}, - Mrnumber = {722297 (84k:58001)}, - Note = {Corrected reprint of the 1971 edition}, - Pages = {ix+272}, - Publisher = {Springer-Verlag}, - Series = {Graduate Texts in Mathematics}, - Title = {Foundations of differentiable manifolds and {L}ie groups}, - Volume = 94, - Year = 1983 -} - -@book{Weibel94, - Address = {Cambridge}, - Author = {Weibel, Charles A.}, - Isbn = {0-521-43500-5; 0-521-55987-1}, - Mrclass = {18-01 (16-01 17-01 20-01 55Uxx)}, - Mrnumber = {1269324 (95f:18001)}, - Mrreviewer = {Kenneth A. Brown}, - Pages = {xiv+450}, - Publisher = {Cambridge University Press}, - Series = {Cambridge Studies in Advanced Mathematics}, - Title = {An introduction to homological algebra}, - Volume = 38, - Year = 1994 -} - -@article{Wie03, - Author = {Wierzba, Jan}, - Fjournal = {Journal of Algebraic Geometry}, - Issn = {1056-3911}, - Journal = {J. Algebraic Geom.}, - Mrclass = {14E15 (14B05 32J18)}, - Mrnumber = {1966025 (2003m:14023)}, - Mrreviewer = {Baohua Fu}, - Number = 3, - Pages = {507--534}, - Title = {Contractions of symplectic varieties}, - Volume = 12, - Year = 2003 -} - -@article{Wil81, - Author = {Wilson, P. M. H.}, - Coden = {CMPMAF}, - Fjournal = {Compositio Mathematica}, - Issn = {0010-437X}, - Journal = {Compositio Math.}, - Mrclass = {14J10 (14J30)}, - Mrnumber = {632435 (83g:14014)}, - Mrreviewer = {Knud L{\o}nsted}, - Note = {\href{http://www.numdam.org/item/CM_1981__43_3_365_0}{numdam.CM_1981__43_3_365_0}}, - Number = 3, - Pages = {365--385}, - Title = {On the canonical ring of algebraic varieties}, - Url = {http://www.numdam.org/item?id=CM_1981__43_3_365_0}, - Volume = 43, - Year = 1981, - Bdsk-Url-1 = {http://www.numdam.org/item?id=CM_1981__43_3_365_0} -} - -@article{Wilson77, - Annote = {Kebekus: Wilson compares the normalisation of a variety with - what you obtain by blowing-up the conductor ideal and gives - conditions on when both are the same. Nice to read, gives a - good example}, - Author = {P.M.H. Wilson}, - Journal = {Math. Proc. Camb. Phil. 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Preprint \href{http://arxiv.org/abs/1210.5564}{arXiv:1210.5564}}, - Number = 3, - Pages = {409--414}, - Title = {Finiteness of algebraic fundamental groups}, - Volume = 150, - Year = 2014 -} - -@Unpublished{YXu18, - author = {Xu, Yanning}, - title = {Summary on {P}roof of {BAB}}, - note = {Preprint \href{http://arxiv.org/abs/1804.07681}{arXiv:1804.07681}}, - month = {April}, - year = 2018 -} - -@article{Ye94, - Author = {Y.-G. Ye}, - Journal = {Invent. Math.}, - Pages = {311--314}, - Title = {A note on complex projective threefolds admitting holomorphic contact structures}, - Volume = 115, - Year = 1994 -} - -@incollection{ZY89, - Author = {Za{\u\i}denberg, Mikhail G. and Lin, Vladimir Y.}, - Booktitle = {Several complex variables. {III}}, - Mrclass = {32-06 (32Axx)}, - Mrnumber = {995071 (89m:32002)}, - Pages = {112--172}, - Publisher = {Springer-Verlag, Berlin}, - Series = {Encyclopaedia Math. Sci.}, - Title = {Finiteness theorems for holomorphic mappings}, - ISBN = {3-540-17005-7}, - Volume = 9, - Year = 1989, - Note = {Translated from the Russian by J. Peetre. \href{https://doi.org/10.1007/978-3-642-61308-1}{DOI:10.1007/978-3-642-61308-1}}, - DOI = {10.1007/978-3-642-61308-1}, - URL = {https://doi.org/10.1007/978-3-642-61308-1} -} - -@book{Zak93, - Address = {Providence, RI}, - Author = {Zak, Fyodor L.}, - Isbn = {0-8218-4585-3}, - Mrclass = {14M07 (14L30 14M17 14N05)}, - Mrnumber = {94i:14053}, - Mrreviewer = {Andrew J. 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Not.}, - FJOURNAL = {International Mathematics Research Notices}, - YEAR = 2006, - PAGES = {1--18}, - ISSN = {1073-7928}, - MRCLASS = {32W20 (32Q15)}, - MRNUMBER = {2233716 (2007b:32058)}, - MRREVIEWER = {S{\l}awomir Ko{\l}odziej}, - NOTE = - {\href{https://doi.org/10.1155/IMRN/2006/63640}{DOI:10.1155/IMRN/2006/63640}}, - DOI = {10.1155/IMRN/2006/63640}, - URL = {https://doi.org/10.1155/IMRN/2006/63640}, -} - -@article{Zhang88, - Author = {Zhang, De-Qi}, - Coden = {OJMAA7}, - Fjournal = {Osaka Journal of Mathematics}, - Issn = {0030-6126}, - Journal = {Osaka J. Math.}, - Mrclass = {14J10 (14J17 14J25)}, - Mrnumber = {957874 (89k:14059)}, - Mrreviewer = {L. B{ă}descu}, - Number = 2, - Pages = {461--497}, - Title = {Logarithmic del {P}ezzo surfaces of rank one with contractible boundaries}, - Volume = 25, - Year = 1988 -} - -@article{Zuo00, - Author = {Zuo, Kang}, - Fjournal = {The Asian Journal of Mathematics}, - Issn = {1093-6106}, - Journal = {Asian J. Math.}, - Mrclass = {32G20 (14D07 32J25)}, - Mrnumber = {1803724 (2002a:32011)}, - Mrreviewer = {Jan Nagel}, - Note = {Kodaira's issue}, - Number = 1, - Pages = {279--301}, - Title = {On the negativity of kernels of {K}odaira-{S}pencer maps on {H}odge bundles and applications}, - Volume = 4, - Year = 2000 -} - -@unpublished{arXiv:1210.2092, - Author = {Campana, Frédéric and Demailly, Jean-Pierre and Peternell, Thomas}, - Month = {October}, - Note = {To appear in the proceedings of the conference 'Recent Advances in Algebraic Geometry', in honour of Robert Lazarsfeld 60th birthday. Preprint \href{http://arxiv.org/abs/1210.2092}{arXiv:1210.2092}.}, - Title = {Rationally connected manifolds and semipositivity of the {R}icci curvature}, - Year = 2012 -} - -@unpublished{arXiv:1301.0915, - Author = {Ou, Wenhao}, - Month = {January}, - Note = {Preprint \href{http://arxiv.org/abs/1301.0915}{arXiv:1301.0915}}, - Title = {Singular rationally connected surfaces with non-zero pluri-forms}, - Year = 2013 -} - -@unpublished{arXiv:1401.2014, - Author = {Ou, Wenhao}, - Month = {January}, - Note = {Preprint \href{http://arxiv.org/abs/1401.2014}{arXiv:1401.2014}}, - Title = {Singular rationally connected threefolds with non-zero pluri-forms}, - Year = 2014 -} - -@unpublished{arXiv:1401.4976, - Author = {Graf, Patrick and Kovács, Sándor J.}, - Month = {January}, - Note = {Preprint - \href{http://arxiv.org/abs/1401.4976}{arXiv:1401.4976}}, - Title = {Potentially {D}u {B}ois spaces}, - Year = 2014 -} - -@phdthesis{arXiv:1401.7495, - Author = {Jörder, Clemens}, - Month = {January}, - Note = {Preprint - \href{http://arxiv.org/abs/1401.7495}{arXiv:1401.7495}}, - School = {Albert-Ludwigs-Universität Freiburg}, - Title = {On the {P}oincaré {L}emma for reflexive differential forms}, - Year = 2014 -} - -@article{cerveaux-lins_neto-annals, - Author = {Cerveau, D. and Lins Neto, A.}, - Fjournal = {Annals of Mathematics. Second Series}, - Journal = {Ann. of Math. (2)}, - Number = 3, - Pages = {577--612}, - Title = {Irreducible components of the space of holomorphic foliations - of degree two in {$\bold C{\rm P}(n)$}, {$n\geq 3$}}, - Volume = 143, - Year = 1996 -} - -@article{deJongStarr, - Author = {de Jong, A. J. and Starr, Jason}, - Coden = {IJMTAW}, - Fjournal = {Illinois Journal of Mathematics}, - Issn = {0019-2082}, - Journal = {Illinois J. Math.}, - Mrclass = {14C05 (14E08)}, - Mrnumber = {2085418 (2006e:14007)}, - Mrreviewer = {A. Prabhakar Rao}, - Note = - {\href{http://projecteuclid.org/euclid.ijm/1258138390}{euclid.ijm/1258138390}}, - Number = 2, - Pages = {415--450}, - Title = {Cubic fourfolds and spaces of rational curves}, - Url = {http://projecteuclid.org/getRecord?id=euclid.ijm/1258138390}, - Volume = 48, - Year = 2004, - Bdsk-Url-1 = {http://projecteuclid.org/getRecord?id=euclid.ijm/1258138390} -} - -@article{deRham52, - Author = {G.~de~Rham}, - Journal = {Comment.~Math.~Helv.}, - Pages = {328--344}, - Title = {Sur la réductibilité d'un espace de Riemann}, - Volume = 26, - Year = 1952 -} - -@article{griffiths-abel, - AUTHOR = {Griffiths, Phillip A.}, - TITLE = {Variations on a theorem of {A}bel}, - JOURNAL = {Invent. Math.}, - FJOURNAL = {Inventiones Mathematicae}, - VOLUME = 35, - YEAR = 1976, - PAGES = {321--390}, - ISSN = {0020-9910}, - NOTE = - {\href{https://doi.org/10.1007/BF01390145}{DOI:10.1007/BF01390145}}, - MRCLASS = {14C25 (32J25 14C30)}, - MRNUMBER = 0435074, - MRREVIEWER = {C. A. M. Peters}, - DOI = {10.1007/BF01390145}, - URL = {https://doi.org/10.1007/BF01390145}, -} - -@book{jouanolou_LNM, - Address = {Berlin}, - Author = {Jouanolou, J. P.}, - Pages = {v+255}, - Publisher = {Springer}, - Series = {Lecture Notes in Mathematics}, - Title = {{É}quations de {P}faff algébriques}, - Volume = 708, - Year = 1979 -} - - -@incollection{revI, - Address = {Berlin}, - Author = {Esnault, Hélène and Viehweg, Eckart}, - Booktitle = {Algebraic threefolds ({V}arenna, 1981)}, - Mrclass = {14E20 (14F10 14H20 14H30)}, - Mrnumber = {672621 (84m:14015)}, - Mrreviewer = {Anatoly Libgober}, - Pages = {241--250}, - Publisher = {Springer}, - Series = {Lecture Notes in Math.}, - Title = {Revêtements cycliques}, - Volume = 947, - Year = 1982 -} - -@article {saito-vanishing, - AUTHOR = {Schnell, Christian}, - TITLE = {On {S}aito's vanishing theorem}, - JOURNAL = {Math. Res. Lett.}, - FJOURNAL = {Mathematical Research Letters}, - VOLUME = 23, - YEAR = 2016, - NOTE = {\href{https://doi.org/10.4310/MRL.2016.v23.n2.a10}{DOI:10.4310/MRL.2016.v23.n2.a10}}, - NUMBER = 2, - PAGES = {499--527}, - ISSN = {1073-2780}, - MRCLASS = {14C30 (32L20 32S35)}, - MRNUMBER = 3512896, - MRREVIEWER = {Tsz On Mario Chan}, - DOI = {10.4310/MRL.2016.v23.n2.a10}, - URL = {https://doi.org/10.4310/MRL.2016.v23.n2.a10}, -} - -@misc{stacks-project, - shorthand = {Stacks}, - author = {The {Stacks Project Authors}}, - title = {Stacks Project}, - howpublished = {Available on the internet at \href{https://stacks.math.columbia.edu}{stacks.math.columbia.edu}}, - year = 2021, -} - -@incollection{voisin-lagrangian, - Address = {Cambridge}, - Author = {Voisin, Claire}, - Booktitle = {Complex projective geometry ({T}rieste, 1989/{B}ergen, 1989)}, - Doi = {10.1017/CBO9780511662652.022}, - Mrclass = {32G10 (32G13 32J27 58F05)}, - Mrnumber = {1201391 (94b:32029)}, - Mrreviewer = {Olivier Debarre}, - Pages = {294--303}, - Publisher = {Cambridge Univ. Press}, - Series = {London Math. Soc. Lecture Note Ser.}, - Title = {Sur la stabilité des sous-variétés lagrangiennes des variétés - symplectiques holomorphes}, - Url = {https://doi.org/10.1017/CBO9780511662652.022}, - Volume = 179, - Year = 1992, - Bdsk-Url-1 = {https://doi.org/10.1017/CBO9780511662652.022} -} - -@book{yellowMonster, - Address = {New York}, - Author = {Hilton, Peter J. and Stammbach, Urs}, - Edition = {Second}, - Isbn = {0-387-94823-6}, - Mrclass = {18-02 (17B56 18Gxx 20J05)}, - Mrnumber = {1438546 (97k:18001)}, - Pages = {xii+364}, - Publisher = {Springer-Verlag}, - Series = {Graduate Texts in Mathematics}, - Title = {A course in homological algebra}, - Volume = 4, - Year = 1997 -} - -@Article{zbMATH00146455, - Author = {Shokurov, Vyacheslav V.}, - Title = {{3-fold log flips. Appendix by Yujiro Kawamata: The minimal - discrepancy coefficients of terminal singularities in - dimension three.}}, - FJournal = {{Russian Academy of Sciences. Izvestiya. Mathematics}}, - Journal = {{Russ. Acad. Sci., Izv., Math.}}, - ISSN = {1064-5632}, - Volume = 40, - Number = 1, - NOTE = {\href{https://doi.org/10.1070/IM1993v040n01ABEH001862}{DOI:10.1070/IM1993v040n01ABEH001862}}, - Pages = {95--202}, - Year = 1992, - Publisher = {Turpion, London}, - Language = {English}, - DOI = {10.1070/IM1993v040n01ABEH001862}, - MSC2010 = {14J30 14E05 14E30}, - Zbl = {0785.14023} -} - -@Book{zbMATH06333926, - Author = {Aigner, Martin and Ziegler, Günter M.}, - Title = {Das BUCH der Beweise}, - Edition = {4th revised and expanded ed.}, - ISBN = {978-3-662-44456-6/hbk; 978-3-662-44457-3/ebook}, - Pages = {viii + 344}, - Year = {2015}, - Publisher = {Heidelberg: Springer Spektrum}, - Language = {German}, - Note = {Mit Zeichnungen von Karl H. Hofmann. \href{https://doi.org/10.1007/978-3-662-57767-7}{DOI:10.1007/978-3-662-57767-7}} -} - -@Book{zbMATH07238313, - Author = {Siegfried {Bosch}}, - Title = {{Algebra}}, - Edition = {9th revised edition}, - ISBN = {978-3-662-61648-2/pbk; 978-3-662-61649-9/ebook}, - Note = {\href{https://doi.org/10.1007/978-3-540-92812-6}{DOI:10.1007/978-3-540-92812-6}}, - Pages = {x + 491}, - Year = {2020}, - Publisher = {Berlin: Springer Spektrum}, - Language = {German}, - MSC2010 = {12-01 12Exx 12Fxx 20-01}, - Zbl = {1440.12001} -} - diff --git a/bibliography/skalpha.bst b/bibliography/skalpha.bst deleted file mode 100644 index d23e09d..0000000 --- a/bibliography/skalpha.bst +++ /dev/null @@ -1,1452 +0,0 @@ -%%% ==================================================================== -%%% @BibTeX-style-file{ -%%% filename = "amsalpha.bst", -%%% version = "2.0", -%%% date = "2000/03/27", -%%% time = "13:49:36 EST", -%%% checksum = "00166 1404 4124 29978", -%%% author = "American Mathematical Society", -%%% address = "American Mathematical Society, -%%% Technical Support, -%%% Electronic Products and Services, -%%% P. 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Copying of this file is -%%% authorized only if either: -%%% (1) you make absolutely no changes to your copy, -%%% including name; OR -%%% (2) if you do make changes, you first rename it -%%% to some other name.", -%%% codetable = "ISO/ASCII", -%%% keywords = "bibtex, bibliography, amslatex, ams-latex", -%%% supported = "yes", -%%% abstract = "BibTeX bibliography style `amsalpha' for BibTeX -%%% versions 0.99a or later and LaTeX version 2e. -%%% Produces alphabetic-label bibliography items in -%%% a form typical for American Mathematical Society -%%% publications.", -%%% docstring = "The checksum field above contains a CRC-16 -%%% checksum as the first value, followed by the -%%% equivalent of the standard UNIX wc (word -%%% count) utility output of lines, words, and -%%% characters. This is produced by Robert -%%% Solovay's checksum utility.", -%%% } -%%% ==================================================================== - -% See the file btxbst.doc for extra documentation other than -% what is included here. And see btxhak.tex for a description -% of the BibTeX language and how to use it. - -% This defines the types of fields that can occur in a database entry -% for this particular bibliography style. Except for `language', -% this is the standard list from alpha.bst. - -%% Types of entries currently allowed in a BibTeX file: -%% -%% ARTICLE -- An article from a journal or magazine. -%% -%% BOOK -- A book with an explicit publisher. -%% -%% BOOKLET -- A work that is printed and bound, -%% but without a named publisher or sponsoring institution. -%% -%% CONFERENCE -- The same as INPROCEEDINGS, -%% included for Scribe compatibility. -%% -%% INBOOK -- A part of a book, -%% which may be a chapter (or section or whatever) and/or a range of pages. -%% -%% INCOLLECTION -- A part of a book having its own title. -%% -%% INPROCEEDINGS -- An article in a conference proceedings. -%% -%% MANUAL -- Technical documentation. -%% -%% MASTERSTHESIS -- A Master's thesis. -%% -%% MISC -- Use this type when nothing else fits. -%% -%% PHDTHESIS -- A PhD thesis. -%% -%% PROCEEDINGS -- The proceedings of a conference. -%% -%% TECHREPORT -- A report published by a school or other institution, -%% usually numbered within a series. -%% -%% UNPUBLISHED -- A document having an author and title, but not formally -%% published. - -ENTRY - { address - author - booktitle - chapter - edition - editor - eprint - howpublished - institution - journal - key - citekey - language - month - mrnumber - note - number - organization - pages - publisher - school - series - title - type - volume - year - longyear - } - {} - { label extra.label sort.label bysame } - -% Removed after.sentence, after.block---not needed. - -INTEGERS { output.state before.all mid.sentence } - -FUNCTION {init.state.consts} -{ #0 'before.all := - #1 'mid.sentence := -} - -% Scratch variables: - -STRINGS { s t } - -% Utility functions - -FUNCTION {shows} -{ duplicate$ ":::: `" swap$ * "'" * top$ -} - -FUNCTION {showstack} -{"STACK=====================================================================" -top$ -stack$ -"ENDSTACK==================================================================" -top$ -} - -FUNCTION {not} -{ { #0 } - { #1 } - if$ -} - -FUNCTION {and} -{ 'skip$ - { pop$ #0 } - if$ -} - -FUNCTION {or} -{ { pop$ #1 } - 'skip$ - if$ -} - -FUNCTION {field.or.null} -{ duplicate$ empty$ - { pop$ "" } - 'skip$ - if$ -} - -FUNCTION {emphasize} -{ duplicate$ empty$ - { pop$ "" } - { "\emph{" swap$ * "}" * } - if$ -} - -FUNCTION {scize} -{ duplicate$ empty$ - { pop$ "" } - { "{\sc " swap$ * "}" * } - if$ -} - -% n.dashify is used to make sure page ranges get the TeX code -% (two hyphens) for en-dashes. - -FUNCTION {n.dashify} -{ 't := - "" - { t empty$ not } - { t #1 #1 substring$ "-" = - { t #1 #2 substring$ "--" = not - { "--" * - t #2 global.max$ substring$ 't := - } - { { t #1 #1 substring$ "-" = } - { "-" * - t #2 global.max$ substring$ 't := - } - while$ - } - if$ - } - { t #1 #1 substring$ * - t #2 global.max$ substring$ 't := - } - if$ - } - while$ -} - -% tie.or.space.connect connects two items with a ~ if the -% second item is less than 3 letters long, otherwise it just puts an -% ordinary space. - -FUNCTION {tie.or.space.connect} -{ duplicate$ text.length$ #3 < - { "~" } - { " " } - if$ - swap$ * * -} - -FUNCTION {add.space.if.necessary} -{ duplicate$ "" = - 'skip$ - { " " * } - if$ -} - -% either.or.check gives a warning if two mutually exclusive fields -% were used in the database. - -FUNCTION {either.or.check} -{ empty$ - 'pop$ - { "can't use both " swap$ * " fields in " * cite$ * warning$ } - if$ -} - -% output.nonnull is called by output. - -FUNCTION {output.nonnull} -% remove the top item from the stack because it's in the way. -{ 's := - output.state mid.sentence = -% If we're in mid-sentence, add a comma to the new top item and write it - { ", " * write$ } -% Otherwise, if we're at the beginning of a bibitem, - { output.state before.all = -% just write out the top item from the stack; - 'write$ -% and the last alternative is that we're at the end of the current -% bibitem, so we add a period to the top stack item and write it out. - { add.period$ " " * write$ } - if$ - mid.sentence 'output.state := - } - if$ -% Put the top item back on the stack that we removed earlier. - s -} - -FUNCTION {output.nonnull.c} -% remove the top item from the stack because it's in the way. -{ 's := - output.state mid.sentence = -% If we're in mid-sentence, add a comma to the new top item and write it - { ": " * write$ } -% Otherwise, if we're at the beginning of a bibitem, - { output.state before.all = -% just write out the top item from the stack; - 'write$ -% and the last alternative is that we're at the end of the current -% bibitem, so we add a period to the top stack item and write it out. - { add.period$ " " * write$ } - if$ - mid.sentence 'output.state := - } - if$ -% Put the top item back on the stack that we removed earlier. - s -} - -% Output checks to see if the stack top is empty; if not, it -% calls output.nonnull to write it out. - -FUNCTION {output} -{ duplicate$ empty$ - 'pop$ - 'output.nonnull - if$ -} - -% Standard warning message for a missing or empty field. For the user -% we call any such field `missing' without respect to the distinction -% made by BibTeX between missing and empty. - -FUNCTION {missing.warning} -{ "missing " swap$ * " in " * cite$ * warning$ } - -% Output.check is like output except that it gives a warning on-screen -% if the given field in the database entry is empty. t is the field -% name. - -FUNCTION {output.check} -{ 't := - duplicate$ empty$ - { pop$ t missing.warning } - 'output.nonnull - if$ -} - -FUNCTION {output.c} -{ 't := - duplicate$ empty$ - { pop$ t missing.warning } - 'output.nonnull.c - if$ -} - -FUNCTION {output.bibitem} -{ newline$ - "\bibitem[" write$ - label write$ - "]{" write$ - cite$ write$ - "}" write$ - newline$ -% This empty string is the first thing that will be written -% the next time write$ is called. Done this way because each -% item is saved on the stack until we find out what punctuation -% should be added after it. Therefore we need an empty first item. - "" - before.all 'output.state := -} - -FUNCTION {output.nonempty.mrnumber} -{ duplicate$ missing$ - { pop$ "" } - 'skip$ - if$ - duplicate$ empty$ - 'pop$ - { " {\sf\scriptsize " swap$ * "}" * write$ } - if$ -} - -FUNCTION {fin.entry} -{ add.period$ - write$ - mrnumber output.nonempty.mrnumber - newline$ -} - -% Removed new.block, new.block.checka, new.block.checkb, new.sentence, -% new.sentence.checka, and new.sentence.checkb functions here, since they -% don't seem to be needed in the AMS style. Also moved some real -% basic functions like `and' and 'or' earlier in the file. - -INTEGERS { nameptr namesleft numnames } - -% The extra section to write out a language field was added -% for AMSPLAIN.BST. Not present in plain.bst. - -FUNCTION {format.language} -{ language empty$ - { "" } - { " (" language * ")" * } - if$ -} - -% This version of format.names puts names in the format -% -% First von Last, Jr. -% -% (i.e., first name first, no abbreviating to initials). - -FUNCTION {format.names} -{ 's := - #1 'nameptr := - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't := - nameptr #1 > - { namesleft #1 > - { ", " * t * } - { numnames #2 > - { "," * } - 'skip$ - if$ - t "others" = - { " et~al." * } - { " and " * t * } - if$ - } - if$ - } - 't - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - - -FUNCTION {format.authors} -{ author empty$ - { "" } - { author format.names scize } - if$ -} - -FUNCTION {format.authors.bysame} -{ author empty$ - { "" } - { bysame "\bysame" = - { bysame } - { author format.names "a" change.case$ scize } - if$ - } - if$ -} - -FUNCTION {format.editors} -{ editor empty$ - { "" } - { editor format.names "a" change.case$ scize - editor num.names$ #1 > - { " (eds.)" * } - { " (ed.)" * } - if$ - } - if$ -} - -FUNCTION {format.nonauthor.editors} -{ editor empty$ - { "" } - { editor format.names - editor num.names$ #1 > - { ", eds." * } - { ", ed." * } - if$ - } - if$ -} - -FUNCTION {format.title} -{ title empty$ - { "" } - { title "t" change.case$ emphasize } - if$ -} - -FUNCTION {format.journal.vol.year} -{ journal empty$ - { "" "journal name" missing.warning } - { journal - volume empty$ - 'skip$ - { " \textbf{" * volume * "}" * } - if$ - year empty$ - { "year" missing.warning } - { " (" * year * ")" * } - if$ - } - if$ -} - -% For formatting the issue number for a journal article. - -FUNCTION {format.number} -{ number empty$ - { "" } - { "no.~" number * } - if$ -} - -% For formatting miscellaneous dates - -FUNCTION {format.date} -{ year empty$ - { month empty$ - { "" } - { "there's a month but no year in " cite$ * warning$ - month - } - if$ - } - { month empty$ - 'year - { month " " * year * } - if$ - } - if$ -} - -%% The volume, series and number information is sort of tricky. -%% This code handles it as follows: -%% If the series is present, and the volume, but not the number, -%% then we do "\emph{Book title}, Series Name, vol. 000" -%% If the series is present, and the number, but not the volume, -%% then we do "\emph{Book title}, Series Name, no. 000" -%% If the series is present, and both number and volume, -%% then we do "\emph{Book title}, vol. XX, Series Name, no. 000" -%% Finally, if the series is absent, -%% then we do "\emph{Book title}, vol. XX" -%% or "\emph{Book title}, no. 000" -%% and if both volume and number are present, give a warning message. - -FUNCTION {format.bookvolume.series.number} -{ volume empty$ - { "" % Push the empty string as a placeholder in case everything else - % is empty too. - series empty$ - 'skip$ - { pop$ series } % if series is not empty put in stack - if$ - number empty$ - 'skip$ - { duplicate$ empty$ % if no preceding material, - 'skip$ % do nothing, otherwise - { ", " * } % add a comma and space to separate. - if$ - "no." number tie.or.space.connect * % add the number information - } - if$ - } -%% If the volume is NOT EMPTY: - { "vol." volume tie.or.space.connect % vol. XX - number empty$ - { series empty$ - 'skip$ - { series ", " * swap$ *} % Series Name, vol. XX - if$ - } - { series empty$ - { "can't use both volume and number if series info is missing" - warning$ - "in BibTeX entry type `" type$ * "'" * top$ - } - { ", " * series * ", no." * number tie.or.space.connect } - if$ - } - if$ - } - if$ - -} % end of format.bookvolume.series.number - -%% format.inproc.title.where.editors is used by inproceedings entry types - -%% No case changing or emphasizing for the title. We want initial -%% caps, roman. -%% We add parentheses around the address (place where conference -%% was held). -%% Likewise we add parentheses around the editors' names. - -FUNCTION {format.inproc.title.address.editors} -{ booktitle empty$ - { "" } - { booktitle - address empty$ - 'skip$ - { add.space.if.necessary "(" * address * ")" * } - if$ - editor empty$ - 'skip$ - { add.space.if.necessary "(" * format.nonauthor.editors * ")" * } - if$ - } - if$ -} - -%% format.incoll.title.editors is similar to format.inproc... but -%% omits the address. For collections that are not proceedings volumes. - -FUNCTION {format.incoll.title.editors} -{ booktitle empty$ - { "" } - { editor empty$ - { booktitle } - { booktitle - add.space.if.necessary "(" * format.nonauthor.editors * ")" * - } - if$ - } - if$ -} - -FUNCTION {format.edition} -{ edition empty$ - { "" } - { output.state mid.sentence = - { edition "l" change.case$ " ed." * } - { edition "t" change.case$ " ed." * } - if$ - } - if$ -} - -INTEGERS { multiresult } - -FUNCTION {multi.page.check} -{ 't := - #0 'multiresult := - { multiresult not - t empty$ not - and - } - { t #1 #1 substring$ - duplicate$ "-" = - swap$ duplicate$ "," = - swap$ "+" = - or or - { #1 'multiresult := } - { t #2 global.max$ substring$ 't := } - if$ - } - while$ - multiresult -} - -FUNCTION {format.pages} -{ pages empty$ - { "" } - { pages n.dashify } - if$ -} - -FUNCTION {format.book.pages} -{ pages empty$ - { "" } - { pages multi.page.check - { "pp.~" pages n.dashify * } - { "p.~" pages * } - if$ - } - if$ -} - -FUNCTION {format.chapter.pages} -{ chapter empty$ - 'format.book.pages - { type empty$ - { "ch.~" } - { type "l" change.case$ " " * } - if$ - chapter * - pages empty$ - 'skip$ - { ", " * format.book.pages * } - if$ - } - if$ -} - -FUNCTION {empty.misc.check} -{ author empty$ title empty$ howpublished empty$ - month empty$ year empty$ note empty$ - and and and and and - key empty$ not and - { "all relevant fields are empty in " cite$ * warning$ } - 'skip$ - if$ -} - -FUNCTION {format.thesis.type} -{ type empty$ - 'skip$ - { pop$ - type "t" change.case$ - } - if$ -} - -FUNCTION {format.tr.number} -{ type empty$ - { "Tech. Report" } - 'type - if$ - number empty$ - { "t" change.case$ } - { number tie.or.space.connect } - if$ -} - -% The format.crossref functions haven't been paid much attention -% at the present time (June 1990) and could probably use some -% work. MJD - -FUNCTION {format.article.crossref} -{ key empty$ - { journal empty$ - { "need key or journal for " cite$ * " to crossref " * crossref * - warning$ - "" - } - { "in " journal * } - if$ - } - { "in " key * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.crossref.editor} -{ editor #1 "{vv~}{ll}" format.name$ - editor num.names$ duplicate$ - #2 > - { pop$ " et~al." * } - { #2 < - 'skip$ - { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = - { " et~al." * } - { " and " * editor #2 "{vv~}{ll}" format.name$ * } - if$ - } - if$ - } - if$ -} - -FUNCTION {format.book.crossref} -{ volume empty$ - { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ - "in " - } - { "vol." volume tie.or.space.connect - " of " * - } - if$ - editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { series empty$ - { "need editor, key, or series for " cite$ * " to crossref " * - crossref * warning$ - "" * - } - { series * } - if$ - } - { key * } - if$ - } - { format.crossref.editor * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.incoll.inproc.crossref} -{ editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { booktitle empty$ - { "need editor, key, or booktitle for " cite$ * " to crossref " * - crossref * warning$ - "" - } - { "in \emph{" booktitle * "}" * } - if$ - } - { "in " key * } - if$ - } - { "in " format.crossref.editor * } - if$ - " \cite{" * crossref * "}" * -} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% The main functions for each entry type. - -% journal, vol and year are formatted together because they are -% not separated by commas. - -FUNCTION {article} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.c - crossref missing$ - { format.journal.vol.year "journal, volume, and year" output.check - format.number output - format.pages "pages" output.check - } - { format.article.crossref output.nonnull - format.pages "pages" output.check - } - if$ - format.language * - note output - fin.entry -} - -FUNCTION {book} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - format.title "title" output.c - format.edition output - crossref missing$ - { format.bookvolume.series.number output - publisher "publisher" output.check - address output - } - { format.book.crossref output.nonnull - } - if$ - format.date "year" output.check - format.language * - note output - fin.entry -} - -FUNCTION {booklet} -{ output.bibitem - format.authors output - format.title "title" output.c - howpublished output - address output - format.date output - note output - fin.entry -} - -FUNCTION {inbook} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - format.title "title" output.c - format.edition output - crossref missing$ - { format.bookvolume.series.number output - format.chapter.pages "chapter and pages" output.check - publisher "publisher" output.check - address output - } - { format.chapter.pages "chapter and pages" output.check - format.book.crossref output.nonnull - } - if$ - format.date "year" output.check - format.language * - note output - fin.entry -} - -FUNCTION {incollection} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.c - crossref missing$ - { format.incoll.title.editors "booktitle" output.check - format.bookvolume.series.number output - publisher "publisher" output.check - address output - format.edition output - format.date "year" output.check - } - { format.incoll.inproc.crossref output.nonnull - } - if$ - note output - format.book.pages output - format.language * - fin.entry -} - -FUNCTION {inproceedings} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.c - crossref missing$ - { format.inproc.title.address.editors "booktitle" output.check - format.bookvolume.series.number output - organization output - publisher output - format.date "year" output.check - } - { format.incoll.inproc.crossref output.nonnull - } - if$ - note output - format.book.pages output - format.language * - fin.entry -} - -FUNCTION {conference} { inproceedings } - -FUNCTION {manual} -{ output.bibitem - author empty$ - { organization empty$ - 'skip$ - { organization output.nonnull - address output - } - if$ - } - { format.authors output.nonnull } - if$ - format.title "title" output.c - author empty$ - { organization empty$ - { address output } - 'skip$ - if$ - } - { organization output - address output - } - if$ - format.edition output - format.date output - note output - fin.entry -} - -FUNCTION {mastersthesis} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.c - "Master's thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.date "year" output.check - note output - format.book.pages output - fin.entry -} - -FUNCTION {misc} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.c - note "note" output.check - format.date output - fin.entry -} - - -FUNCTION {phdthesis} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.c - "Ph.D. thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.date "year" output.check - note output - format.book.pages output - fin.entry -} - -FUNCTION {proceedings} -{ output.bibitem - editor empty$ - { organization output } - { format.editors output.nonnull } - if$ - format.title "title" output.c - format.bookvolume.series.number output - address empty$ - { editor empty$ - 'skip$ - { organization output } - if$ - publisher output - format.date "year" output.check - } - { address output.nonnull - editor empty$ - 'skip$ - { organization output } - if$ - publisher output - format.date "year" output.check - } - if$ - note output - fin.entry -} - -FUNCTION {techreport} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.c - format.tr.number output.nonnull - institution "institution" output.check - address output - format.date "year" output.check - note output - fin.entry -} - -FUNCTION {unpublished} -{ output.bibitem - format.authors "author" output.check - format.title "title" output.c - note "note" output.check - format.date output - fin.entry -} - -FUNCTION {default.type} { misc } - -MACRO {jan} {"January"} - -MACRO {feb} {"February"} - -MACRO {mar} {"March"} - -MACRO {apr} {"April"} - -MACRO {may} {"May"} - -MACRO {jun} {"June"} - -MACRO {jul} {"July"} - -MACRO {aug} {"August"} - -MACRO {sep} {"September"} - -MACRO {oct} {"October"} - -MACRO {nov} {"November"} - -MACRO {dec} {"December"} - -READ - -FUNCTION {sortify} -{ purify$ - "l" change.case$ -} - -INTEGERS { len } - -FUNCTION {chop.word} -{ 's := - 'len := - s #1 len substring$ = - { s len #1 + global.max$ substring$ } - 's - if$ -} - -INTEGERS { et.al.char.used } - -FUNCTION {initialize.et.al.char.used} -{ #0 'et.al.char.used := -} - -EXECUTE {initialize.et.al.char.used} - -FUNCTION {format.lab.names} -{ 's := - s num.names$ 'numnames := - numnames #1 > - { numnames #4 > - { #3 'namesleft := } - { numnames 'namesleft := } - if$ - #1 'nameptr := - "" - { namesleft #0 > } - { nameptr numnames = - { s nameptr "{ff }{vv }{ll}{ jj}" format.name$ "others" = - { "{\etalchar{+}}" * - #1 'et.al.char.used := - } - { s nameptr "{v{}}{l{}}" format.name$ * } - if$ - } - { s nameptr "{v{}}{l{}}" format.name$ * } - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ - numnames #4 > - { "{\etalchar{+}}" * - #1 'et.al.char.used := - } - 'skip$ - if$ - } - { s #1 "{v{}}{l{}}" format.name$ - duplicate$ text.length$ #2 < - { pop$ s #1 "{ll}" format.name$ #3 text.prefix$ } - 'skip$ - if$ - } - if$ -} - -FUNCTION {author.key.label} -{ author empty$ - { key empty$ - { cite$ #1 #3 substring$ } - { key #3 text.prefix$ } - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {author.editor.key.label} -{ author empty$ - { editor empty$ - { key empty$ - { cite$ #1 #3 substring$ } - { key #3 text.prefix$ } - if$ - } - { editor format.lab.names } - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {author.key.organization.label} -{ author empty$ - { key empty$ - { organization empty$ - { cite$ #1 #3 substring$ } - { "The " #4 organization chop.word #3 text.prefix$ } - if$ - } - { key #3 text.prefix$ } - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {editor.key.organization.label} -{ editor empty$ - { key empty$ - { organization empty$ - { cite$ #1 #3 substring$ } - { "The " #4 organization chop.word #3 text.prefix$ } - if$ - } - { key #3 text.prefix$ } - if$ - } - { editor format.lab.names } - if$ -} - -FUNCTION {calc.label} -{ type$ "book" = - type$ "inbook" = - or - 'author.editor.key.label - { type$ "proceedings" = - 'editor.key.organization.label - { type$ "manual" = - 'author.key.organization.label - 'author.key.label - if$ - } - if$ - } - if$ - duplicate$ - longyear field.or.null purify$ #-1 #2 substring$ - * - year field.or.null purify$ #-1 #2 substring$ - * - 'label := - year field.or.null purify$ #-1 #4 substring$ - * - sortify 'sort.label := -} - -FUNCTION {sort.format.names} -{ 's := - #1 'nameptr := - "" - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { nameptr #1 > - { " " * } - 'skip$ - if$ - s nameptr "{vv{ } }{ll{ }}{ ff{ }}{ jj{ }}" format.name$ 't := - nameptr numnames = t "others" = and - { "et al" * } - { t sortify * } - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {sort.format.title} -{ 't := - "A " #2 - "An " #3 - "The " #4 t chop.word - chop.word - chop.word - sortify - #1 global.max$ substring$ -} - -FUNCTION {author.sort} -{ author empty$ - { key empty$ - { "to sort, need author or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {author.editor.sort} -{ author empty$ - { editor empty$ - { key empty$ - { "to sort, need author, editor, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { editor sort.format.names } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {author.organization.sort} -{ author empty$ - { organization empty$ - { key empty$ - { "to sort, need author, organization, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { "The " #4 organization chop.word sortify } - if$ - } - { author sort.format.names } - if$ -} - -FUNCTION {editor.organization.sort} -{ editor empty$ - { organization empty$ - { key empty$ - { "to sort, need editor, organization, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { "The " #4 organization chop.word sortify } - if$ - } - { editor sort.format.names } - if$ -} - -FUNCTION {presort} -{ - sort.label - calc.label - " " - * - type$ "book" = - type$ "inbook" = - or - 'author.editor.sort - { type$ "proceedings" = - 'editor.organization.sort - { type$ "manual" = - 'author.organization.sort - 'author.sort - if$ - } - if$ - } - if$ - * - " " - * - year field.or.null sortify - * - " " - * - title field.or.null - sort.format.title - * - #1 entry.max$ substring$ - 'sort.key$ := -} - -ITERATE {presort} - -SORT - -STRINGS { - longest.label last.sort.label next.extra prev.author this.author -} - -INTEGERS { longest.label.width last.extra.num } - -FUNCTION {initialize.longest.label} -{ "" 'longest.label := - #0 int.to.chr$ 'last.sort.label := - "" 'next.extra := - #0 'longest.label.width := - #0 'last.extra.num := - "abcxyz" 'prev.author := - "" 'this.author := -} - -FUNCTION {forward.pass} -{ last.sort.label sort.label = - { last.extra.num #1 + 'last.extra.num := - last.extra.num int.to.chr$ 'extra.label := - } - { "a" chr.to.int$ 'last.extra.num := - "" 'extra.label := - sort.label 'last.sort.label := - } - if$ - author empty$ { editor empty$ { "" } 'editor if$ } 'author if$ - 'this.author := - this.author prev.author = - { "\bysame" 'bysame := } - { "" 'bysame := - this.author "" = - { "abcxyz" } - 'this.author - if$ - 'prev.author := - } - if$ -} - -FUNCTION {reverse.pass} -{ next.extra "b" = - { "a" 'extra.label := } - 'skip$ - if$ - label extra.label * 'label := - label width$ longest.label.width > - { label 'longest.label := - label width$ 'longest.label.width := - } - 'skip$ - if$ - extra.label 'next.extra := -} - -EXECUTE {initialize.longest.label} - -ITERATE {forward.pass} - -REVERSE {reverse.pass} - -FUNCTION {begin.bib} -{ et.al.char.used - { "\newcommand{\etalchar}[1]{$^{#1}$}" write$ newline$ } - 'skip$ - if$ - preamble$ empty$ - 'skip$ - { preamble$ write$ newline$ } - if$ - "\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}" - write$ newline$ - "\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR}" - write$ newline$ - "% \MRhref is called by the amsart/book/proc definition of \MR." - write$ newline$ - "\providecommand{\MRhref}[2]{%" - write$ newline$ - " \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}" - write$ newline$ - "}" - write$ newline$ - "\providecommand{\href}[2]{#2}" - write$ newline$ - "\begin{thebibliography}{" longest.label * "}" * - write$ newline$ -} - -EXECUTE {begin.bib} - -EXECUTE {init.state.consts} - -ITERATE {call.type$} - -FUNCTION {end.bib} -{ newline$ - "\end{thebibliography}" write$ newline$ -} - -EXECUTE {end.bib} -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} diff --git a/tex b/tex new file mode 160000 index 0000000..6b3482d --- /dev/null +++ b/tex @@ -0,0 +1 @@ +Subproject commit 6b3482d50e8051a2ffdc32d3891b734f0ae1e3da