Clean up

.vscode/ltex.dictionary.en-US.txt

@@ -79,3 +79,9 @@ Delcroix
 Székelyhidi
 Tosatti
 Chiu
+Oberwolfach
+Conlon
+Daskalopoulos
+Mese
+Nevanlinna
+arithmetics

MFO26.tex

@@ -54,100 +54,84 @@
 \maketitle
 
 
+\section{Workshop Title}
+Komplexe Analysis --- Differential and Metric Methods in the Theory of Kähler Spaces
+
+\section{Proposed Organisers}
+
+\begin{tabular}{ll}
+  \parbox[t]{7cm}{
+    Eleonora Di Nezza\\
+    IMJ-PRG, Sorbonne Université,\\
+    4 Place Jussieu\\
+     75005 Paris\\
+      France\\[2mm]
+    \href{mailto:eleonora.dinezza@imj-prg.fr}{eleonora.dinezza@imj-prg.fr}} &
+  \parbox[t]{7cm}{
+    Stefan Kebekus\\
+    Albert-Ludwigs-Universität Freiburg\\
+    Ernst-Zermelo-Straße 1\\
+    79104 Freiburg\\
+    Germany\\[2mm]
+    \href{mailto:stefan.kebekus@math.uni-freiburg.de}{stefan.kebekus@math.uni-freiburg.de}}    
+    \\
+  \ \\
+  \ \\
+ \parbox[t]{6cm}{
+    Mihai Păun \\
+    Universität Bayreuth \\
+    Universitätsstraße 30\\
+    95447 Bayreuth\\
+    Germany\\[2mm]
+    \href{mailto:mihai.paun@uni-bayreuth.de}{mihai.paun@uni-bayreuth.de}}
+ &
+  \parbox[t]{6cm}{
+    Stefan Schreieder\\
+    Leibniz Universit\"at Hannover \\
+    Welfengarten 1\\
+    30167 Hannover\\
+    Germany\\[2mm]
+    \href{mailto:schreieder@math.uni-hannover.de}{schreieder@math.uni-hannover.de}}
+\end{tabular}
 
 
+\section{Abstract}
 
+Complex Analysis is a very active branch of mathematics with applications in many other fields. 
+The proposed workshop presents recent results in complex
+analysis and surveys progress in topics that link the field to other branches of mathematics.  
+%This application highlights differential-geometric methods in the study of singular spaces, the interplay between analytic and algebraic methods, and the relation between complex analysis and Scholze-Clausen's condensed mathematics.
+
+%The meeting has always been a venue where confirmed researchers from different backgrounds meet and where young mathematicians are giving their first talks at an international conference.  While we are happy to see a growing number of talented, young researchers, we feel that this age group suffers the most from the ongoing COVID crisis and the resulting lack of exchange and interaction.  We would therefore like to emphasize the contributions of younger researchers and invite a relatively higher number of them.  We are looking forward to welcoming them to Oberwolfach, rediscover the pleasure of meeting in person, and exchange points of view!
+
+
+\section{Mathematics Subject Classification}
+
+\subsubsection*{2020 Mathematics Subject Classification}
+
+\begin{tabular}{llll}
+Primary   & 32 &--& Several complex variables and analytic spaces\\
+Secondary & 14 &--& Algebraic geometry \\
+          & 53 &--& Differential geometry \\
+          & 58 &--& Global analysis, analysis on manifolds 
+\end{tabular}
 
 
 \section{Description of the Workshop}
 
+The proposed workshop presents recent results in Complex Geometry and surveys
+relations to other fields. For 2026, we would like to emphasize the fields
+described below.  
+Each relates to complex analysis differently.  
+Each has seen substantial progress recently, producing results that will be of importance for years to come.  
+%The bullet items list some of the latest developments that have attracted our attention.
 
-% Topology of Kähler spaces: D-modules, perverse sheaves, Hodge modules
+%We plan to include at least one broader overview talk for each of the three subjects, as well as more specialized presentations by senior experts and junior researchers.  
-%
+We will account for new developments that arise between the time of submission
-%  
+of this proposal and the time of the workshop.  Following good Oberwolfach
-%- Singularities and Hodge ideals etc: Mustata-Popa, Park, Ruijie Yang, Schnell 
+tradition, we will keep the number of talks small to provide ample opportunity
-%
+for informal discussions. 
-%- Lagrangian fibrations: Maulik-Shen, Shen-Yin, Schnell, Bakker
+%After so many months of the pandemic, this will be more than welcome!
-%
-%- Singer-Hopf conjecture and fundamental groups of Kaehler manifolds: Arapura, Botong Wang, Maxim, Llosa-Isenrich—Py.
-
-
-\subsection{Topology of Kähler spaces: D-modules, perverse sheaves, Hodge modules}
-
-Over the last decade, Saito's theory of Hodge modules has seen spectacular
-applications in birational geometry.  More recent developments, which are of
-significant importance, connect the theory to singularity theory, commutative
-algebra, and the topology of algebraic varieties.  The following topics in this
-area will particularly interest our workshop.
-
-
-\subsubsection{Singularities and Hodge Ideals}
-
-In a series of influential papers starting with \cite{MR4081135}, Mustaţă and
-Popa used Hodge modules to refine and generalize well-known invariants of
-singularities, most notably the multiplier ideals used in analysis and algebraic
-geometry. Schnell and Yang’s recent preprint \cite{arXiv:2309.16763} suggested
-an alternative approach toward similar ends.  The first applications pertain to
-Bernstein--Sato polynomials and their zero sets; these are essential invariants
-of singularities originating from commutative algebra that are hard to compute.
-Schnell and Yang apply their results to conjectures of
-Debarre--Casalaina-Martin--Grushevsky concerning the Riemann--Schottky problem
-and the singularities of Theta divisors of principally polarized Abelian
-varieties. 
-
-Park and Popa recently applied perverse sheaves and D-module theory to improve
-Goresky--MacPherson's classic Lefschetz theorems in the singular setting. A
-program put forward by Friedman--Laza aims at understanding the Hodge structures
-of degenerating Calabi--Yau varieties. 
-
-
-\subsubsection{Lagrangian fibrations}
-
-A Lagrangian fibration of a hyperkähler manifold $M$ is a proper holomorphic map
-$f : M \to B$ whose generic fibers are Langrangian. 
-
-
-\paragraph{Compact Setting}
-
-If $M$ is compact, a well-known conjecture in the field predicts that $B$ is
-projective space.  In the case where $B$ is smooth, Hwang established the
-conjecture more than 16 years ago in a celebrated paper.  There is new insight
-today, as Bakker--Schnell recently found a purely Hodge theoretic proof of
-Hwang's result in \cite{arXiv:2311.08977}.  Hopefully, these methods will give
-insight into the singular setting, which remains open to date.
-
-
-\paragraph{Non-compact Setting}
-
-Geometers study Lagrangian fibrations over non-compact bases in the framework of
-the ``$P=W$ conjecture,'' which Maulik--Shen and Hausel--Mellit--Minets--Schiffmann
-have recently proved \cite{arXiv:2209.02568, arXiv:2209.05429}.  In the same
-setting, Shen–Yin discovered a remarkable symmetry of certain pushforward
-sheaves and conjectured that more general symmetries exist. Schnell has recently
-established these conjectures in \cite{arXiv:2303.05364} and also proved two
-conjectures of Maulik–Shen–Yin on the behavior of certain perverse sheaves near
-singular fibers.
-
-
-\subsubsection{Singer--Hopf conjecture and fundamental groups of Kähler manifolds}
-
-The Singer-Hopf conjecture asserts that a closed aspherical manifold of real
-dimension $2n$ has positive signed Euler characteristic, $(-1)^n \cdot
-\chi(X)\geq 0$. This conjecture goes back to 1931 when Hopf formulated a related
-version for Riemannian manifolds. Recently, Arapura–Maxim–Wang suggested
-Hodge-theoretic refinements of this conjecture for Kähler manifolds in
-\cite{arXiv:2310.14131}. While the methods of \cite{arXiv:2310.14131} suffice to
-show particular cases, the statement remains open in full generality. 
-
-In a related direction, Llosa-Isenrich--Py found an application of complex
-geometry and Hodge theory to geometric group theory, settling an old question of
-Brady on the finiteness properties of groups \cite{zbMATH07790946}. As a
-byproduct, the authors also obtain a proof of the classical Singer conjecture in
-an essential particular case in the realm of Kähler manifolds.
-
-Our goal in this workshop is to bring together several experts in geometric
-group theory with experts on Hodge theory and to explore further potential
-applications of the methods from one field to problems in the other.
 
 
 \subsection{Canonical Metrics and Hyperbolicity}
@@ -156,16 +140,16 @@ applications of the methods from one field to problems in the other.
 
 In the proof of the Donaldson--Tian--Yau conjecture, which Chen--Donaldson--Sun
 gave in a series of papers around 2015, Kähler--Einstein metrics with conic
-singularities along a smooth divisor emerged to play a vital role. Since then,
+singularities along a smooth divisor emerged to play a vital role.  The work of
-these metrics have become an object of study in their own right.  The work of
 Brendle, Donaldson, Guenancia, Rubinstein, and many others provides a complete
 package of results that generalize Yau's celebrated solution of the Calabi
-conjecture to the conic setting.  Today, many exciting recent developments in
+conjecture to the conic setting.  Since then, these metrics have become an
+object of study in their own right.  Today, many exciting recent developments in
 this field gravitate around the following general question.
 
 \begin{q}
-  Let $X$ be a projective manifold, and let $D\subset $ be a non-singular
+  Let $X$ be a projective manifold, and let $D \subsetneq X$ be a non-singular
-  divisor.  Assume that for every sufficiently small angle $0< \beta << 1$,
+  divisor.  Assume that for every sufficiently small angle $0 < \beta \ll 1$,
   there exists a unique Kähler--Einstein metric $\omega_\beta$ with conic
   singularities of angle $2\pi\beta$ along $D$.  In other words, assume that
   \[
@@ -177,9 +161,9 @@ this field gravitate around the following general question.
   rescaling?
 \end{q}
 
-Starting with \cite{zbMATH07615186}, a series of articles by Biquard--Guenancia
+In \cite{zbMATH07615186} and the very recent preprint \cite{arXiv:2407.01150},
-settles many relevant (and technically challenging!) particular cases of this
+Biquard--Guenancia begin settling relevant (and technically challenging!)
-question.
+particular cases of this question.
 \begin{itemize}
   \item If $(X,D)$ is the toroidal compactification of a ball quotient, then the
   limit of the metric exists and equals the hyperbolic metric.
@@ -216,43 +200,11 @@ metric.  Using the bounded geometry method, Datar--Fu--Song recently showed an
 analogous result in the case of isolated log canonical singularities
 \cite{zbMATH07669617}.  Fu–Hein–Jiang obtained precise asymptotics shortly
 after, \cite{zbMATH07782497}. Essential contributions directly connected to
-these topics are due to Chiu, Delcroix, Hein, C.~Li, Y.~Li, Sun, Székelyhidi,
+these topics are due to Chiu--Székelyhidi \cite{zbMATH07810677}, Delcroix,
-Tosatti, and Zhang.
+Conlon--Hein \cite{zbMATH07858206}, C.~Li, Y.~Li, Tosatti and Zhang.
-
-\bigskip
-
-{\color{red}\textbf --- DO NOT READ ANYTHING BELOW THIS LINE ---}
 
 
-\subsubsection{Complex hyperbolicity}
+\subsubsection{Complex Hyperbolicity}
-
-The Green-Griffiths conjecture (concerning the Zariski closure of holomorphic
-entire curves or more generally, of families of holomorphic disks on varieties
-of general type) continues to keep busy many complex geometers. Probably the
-most complete result in this field is due to A. Bloch (more than 100 years ago),
-who -in modern language- showed that the Zariski closure of a map $\varphi:
-\mathbb C \to A$ to a complex tori $A$ is the translate of a sub-tori. A decade
-ago, K.~Yamanoi established the Green-Griffiths conjecture for projective
-manifolds general type, which admit a generically finite map into an Abelian
-variety. This represents a very nice generalization of Bloch's theorem.
-
-In the last couple of years the field is taking a very interesting direction, by
-combining techniques from Hodge theory with the familiar Nevanlinna theory and
-jet differentials, cf. the articles by D. Brotbek, Y. Deng, Y. Brunebarbe, B.
-Cadorel and A. Javanpeykar.
-
-Using recent advances in the theory of harmonic maps (due to
-Daskalopoulos-Mese), Y. Deng and K. Yamanoi were able to confirm the
-Green-Griffiths conjecture for manifolds whose fundamental group admits a
-representation having certain natural properties (echoing the case of curves of
-genus at least two). 
-
-Techniques from birational geometry, in connection with the work of F.~Campana
-are also present in the field via the -long awaited- work of E. Rousseau and its
-collaborators. 
-
-
-\subsubsection{Complex hyperbolicity. Mark II}
 
 The 1979 Green-Griffiths-Lang conjecture asserts that every complex-projective
 variety $X$ of general type contains a proper subvariety $Y \subsetneq X$, such
@@ -260,10 +212,15 @@ that every non-constant entire holomorphic curve $\mathbb C \to X$ takes its
 values in $Y$.  Its beginnings date back to 1926, when André Bloch showed that
 the Zariski closure of entire holomorphic curve $\varphi: \mathbb C \to A$ to a
 complex torus $A$ is the translate of a sub-torus. Today, the conjecture still
-drives much of the research in complex geometry. We highlight several advances
+drives substantial research in complex geometry.  Several authors, including
-that will be relevant for our workshop.
+Brotbek, Brunebarbe, Deng, Cadorel, and Javanpeykar, opened a new research
+direction with relation to arithmetic, by combining techniques from Hodge theory
+with Nevanlinna theory and jet differentials, \cite{arXiv:2007.12957,
+arXiv:2207.03283, arXiv:2305.09613}. Besides, we highlight two additional
+advances that will be relevant for our workshop.
 
-\paragraph{Hypersurfaces in projective space}
+
+\paragraph{Hypersurfaces in Projective Space}
 
 A remarkable paper of Bérczi and Kirwan, \cite{MR4688701} published in September
 last year, establishes hyperbolicity and proves the Green-Griffiths-Lang for
@@ -274,26 +231,100 @@ non-polynomial bounds of order $(\sqrt{n} \log n)^n$ or worse.  The proof builds
 on a strategy of Diverio-Merker-Rousseau and combines non-reductive geometric
 invariant theory with the ``Grassmannian techniques'' of Riedl-Yang.  A very
 recent preprint of Cadorel simplifies the proof Bérczi-Kirwan substantially, but
-still needs to undergo peer review, \cite{arXiv:2406.19003}.
+still needs to undergo a peer review, \cite{arXiv:2406.19003}.
 
 
-\paragraph{Hyperbolicity and representations of fundamental groups}
+\paragraph{Representations of Fundamental Groups}
 
-Using recent advances in the theory of harmonic maps (due to
+Using recent advances in the theory of harmonic maps due to Daskalopoulos--Mese
-Daskalopoulos-Mese), Y. Deng and K. Yamanoi were able to confirm the
+\cite{arXiv:2112.13961}, Deng--Yamanoi were able to confirm the Green--Griffiths
-Green-Griffiths conjecture for manifolds whose fundamental group admits a
+conjecture for manifolds whose fundamental group admits a representation having
-representation having certain natural properties (echoing the case of curves of
+certain natural properties, in direct analogy to the case of general-type
-genus at least two). 
+curves. 
 
 
-\paragraph{Material collections}
+\subsection{Topology and Hodge Theory of Kähler spaces}
+
+Ever since its invention, Hodge theory has been one of the most powerful tools
+in studying the geometry and topology of Kähler spaces.  More recent
+developments connect the theory to singularity theory, commutative algebra, and
+the topology of algebraic varieties.  The following topics in this area will
+particularly interest our workshop. 
 
 
+\subsubsection{Singularities and Hodge Ideals}
 
-In the last couple of years the field is taking a very interesting direction, by
+In a series of influential papers starting with \cite{MR4081135}, Mustaţă and
-combining techniques from Hodge theory with the familiar Nevanlinna theory and
+Popa used Hodge modules to refine and generalize well-known invariants of
-jet differentials, cf. the articles by D. Brotbek, Y. Deng, Y. Brunebarbe, B.
+singularities, most notably the multiplier ideals used in analysis and algebraic
-Cadorel and A. Javanpeykar.
+geometry. Schnell and Yang’s recent preprint \cite{arXiv:2309.16763} suggested
+an alternative approach toward similar ends.  The first applications pertain to
+Bernstein--Sato polynomials and their zero sets; these are essential invariants
+of singularities originating from commutative algebra that are hard to compute.
+Schnell and Yang apply their results to conjectures of
+Debarre--Casalaina-Martin--Grushevsky concerning the Riemann--Schottky problem
+and the singularities of Theta divisors of principally polarized Abelian
+varieties. 
+
+Park and Popa recently applied perverse sheaves and D-module theory to improve
+Goresky--MacPherson's classic Lefschetz theorems in the singular setting. A
+program put forward by Friedman--Laza aims at understanding the Hodge structures
+of degenerating Calabi--Yau varieties. 
+
+
+\subsubsection{Lagrangian Fibrations}
+
+A Lagrangian fibration of a hyperkähler manifold $M$ is a proper holomorphic map
+$f : M \to B$ whose generic fibers are Langrangian. 
+
+
+\paragraph{Compact Setting}
+
+If $M$ is compact, a well-known conjecture in the field predicts that $B$ is
+projective space.  In the case where $B$ is smooth, Hwang established the
+conjecture more than 16 years ago in a celebrated paper.  There is new insight
+today, as Bakker--Schnell recently found a purely Hodge theoretic proof of
+Hwang's result in \cite{arXiv:2311.08977}.  Hopefully, these methods will give
+insight into the singular setting, which remains open to date.
+
+
+\paragraph{Non-compact Setting}
+
+Geometers study Lagrangian fibrations over non-compact bases in the framework of
+the ``$P=W$ conjecture,'' which Maulik--Shen and Hausel--Mellit--Minets--Schiffmann
+have recently proved \cite{arXiv:2209.02568, arXiv:2209.05429}.  In the same
+setting, Shen–Yin discovered a remarkable symmetry of certain pushforward
+sheaves and conjectured that more general symmetries exist. Schnell has recently
+established these conjectures in \cite{arXiv:2303.05364} and also proved two
+conjectures of Maulik–Shen–Yin on the behavior of certain perverse sheaves near
+singular fibers.
+
+
+\subsubsection{Singer--Hopf Conjecture and Fundamental Groups of Kähler Manifolds}
+
+The Singer-Hopf conjecture asserts that a closed aspherical manifold of real
+dimension $2n$ has positive signed Euler characteristic, $(-1)^n \cdot
+\chi(X)\geq 0$. This conjecture goes back to 1931 when Hopf formulated a related
+version for Riemannian manifolds. Recently, Arapura–Maxim–Wang suggested
+Hodge-theoretic refinements of this conjecture for Kähler manifolds in
+\cite{arXiv:2310.14131}. While the methods of \cite{arXiv:2310.14131} suffice to
+show particular cases, the statement remains open in full generality. 
+
+In a related direction, Llosa-Isenrich--Py found an application of complex
+geometry and Hodge theory to geometric group theory, settling an old question of
+Brady on the finiteness properties of groups \cite{zbMATH07790946}. As a
+byproduct, the authors also obtain a proof of the classical Singer conjecture in
+an essential particular case in the realm of Kähler manifolds.
+
+Our goal in this workshop is to bring together several experts in geometric
+group theory with experts on Hodge theory and to explore further potential
+applications of the methods from one field to problems in the other.
+
+
+\section{Suggested and Excluded Dates}
+
+We would prefer if our workshop took place in mid of September or early to mid
+of April.
 
 
 

general.bib

@@ -1,3 +1,87 @@
+@misc{arXiv:2207.03283,
+      title={Hyperbolicity in presence of a large local system}, 
+      author={Yohan Brunebarbe},
+      month={July},
+      year={2022},
+      note={Preprint \href{https://arxiv.org/abs/2207.03283}{arXiv:2207.03283}},
+      archivePrefix={arXiv},
+      primaryClass={math.AG},
+      url={https://arxiv.org/abs/2207.03283}, 
+}
+
+@misc{arXiv:2305.09613,
+      title={The relative {G}reen-{G}riffiths-{L}ang conjecture for families of varieties of maximal {A}lbanese dimension}, 
+      author={Yohan Brunebarbe},
+      month={May},
+      year={2023},
+      note={Preprint \href{https://arxiv.org/abs/2305.09613}{arXiv:2305.09613}},
+      archivePrefix={arXiv},
+      primaryClass={math.AG},
+      url={https://arxiv.org/abs/2305.09613}, 
+}
+
+@misc{arXiv:2007.12957,
+      title={Arakelov-{N}evanlinna inequalities for variations of {H}odge structures and applications}, 
+      author={Damian Brotbek and Yohan Brunebarbe},
+      month={July},
+      year={2020},
+      note={Preprint \href{https://arxiv.org/abs/2007.12957}{arXiv:2007.12957}},
+      archivePrefix={arXiv},
+      primaryClass={math.AG},
+      url={https://arxiv.org/abs/2007.12957}, 
+}
+
+@misc{arXiv:2112.13961,
+      title={Infinite energy maps and rigidity}, 
+      author={Daskalopoulos, Georgios and Mese, Chikako},
+      month={December},
+      year={2021},
+      note={Preprint \href{https://arxiv.org/abs/2112.13961}{arXiv:2112.13961}},
+      url={https://arxiv.org/abs/2112.13961}
+}
+
+@Article{zbMATH07858206,
+ Author = {Conlon, Ronan J. and Hein, Hans-Joachim},
+ Title = {Classification of asymptotically conical {Calabi}-{Yau} manifolds},
+ FJournal = {Duke Mathematical Journal},
+ Journal = {Duke Math. J.},
+ ISSN = {0012-7094},
+ Volume = {173},
+ Number = {5},
+ Pages = {947--1015},
+ Year = {2024},
+ Language = {English},
+ DOI = {10.1215/00127094-2023-0030},
+ Keywords = {53C25,14J32},
+ zbMATH = {7858206}
+}
+
+@Article{zbMATH07810677,
+ Author = {Chiu, Shih-Kai and Sz{\'e}kelyhidi, G{\'a}bor},
+ Title = {Higher regularity for singular {K{\"a}hler}-{Einstein} metrics},
+ FJournal = {Duke Mathematical Journal},
+ Journal = {Duke Math. J.},
+ ISSN = {0012-7094},
+ Volume = {172},
+ Number = {18},
+ Pages = {3521--3558},
+ Year = {2023},
+ Language = {English},
+ DOI = {10.1215/00127094-2022-0107},
+ Keywords = {32Q20,32Q25,53C25},
+ URL = {projecteuclid.org/journals/duke-mathematical-journal/volume-172/issue-18/Higher-regularity-for-singular-K%c3%a4hlerEinstein-metrics/10.1215/00127094-2022-0107.full},
+ zbMATH = {7810677}
+}
+
+@misc{arXiv:2407.01150,
+      title={Degenerating conic {K}ähler-{E}instein metrics to the normal cone}, 
+      author={Biquard, Olivier and Guenancia, Henri},
+      note={Preprint \href{https://arxiv.org/abs/2407.01150}{arXiv:2407.01150}},
+      year={2024},
+      month={July},
+      url={https://arxiv.org/abs/2407.01150},
+}
+
 @Article{zbMATH07782497,
  Author = {Fu, Xin and Hein, Hans-Joachim and Jiang, Xumin},
  Title = {Asymptotics of {K{\"a}hler}-{Einstein} metrics on complex hyperbolic cusps},
@@ -50,10 +134,11 @@
 }
 
 @misc{arXiv:2401.03935,
-      title={Continuity of solutions to complex Monge-Amp\`{e}re equations on compact K\"{a}hler spaces}, 
+      title={Continuity of solutions to complex {M}onge-{A}mpère equations on compact {K}ähler spaces}, 
       author={Ye-Won Luke Cho and Young-Jun Choi},
+      month={January},
       year={2024},
-      eprint={2401.03935},
+      note={Preprint \href{https://arxiv.org/abs/2401.03935}{arXiv:2401.03935}},
       archivePrefix={arXiv},
       primaryClass={math.DG},
       url={https://arxiv.org/abs/2401.03935}, 
@@ -146,9 +231,11 @@
 
 
 @misc{arXiv:2310.14131,
-      title={Hodge-theoretic variants of the Hopf and Singer Conjectures}, 
+      title={Hodge-theoretic variants of the {H}opf and {S}inger {C}onjectures}, 
       author={Donu Arapura and Laurentiu Maxim and Botong Wang},
-      year={2024},
+      note={Preprint \href{https://arxiv.org/abs/2310.14131}{arXiv:2310.14131}},
+      month={October},
+      year={2023},
       eprint={2310.14131},
       archivePrefix={arXiv},
       primaryClass={math.AG},
@@ -156,40 +243,44 @@
 }
 
 @misc{arXiv:2303.05364,
-      title={Hodge theory and Lagrangian fibrations on holomorphic symplectic manifolds}, 
+      title={Hodge theory and {L}agrangian fibrations on holomorphic symplectic manifolds}, 
       author={Christian Schnell},
+      month={March},
       year={2023},
-      eprint={2303.05364},
+      note={Preprint \href{https://arxiv.org/abs/2303.05364}{arXiv:2303.05364}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2303.05364}, 
 }
 
 @misc{arXiv:2209.05429,
-      title={$P=W$ via $H_2$}, 
+      title={{$P=W$} via {$H_2$}}, 
       author={Tamas Hausel and Anton Mellit and Alexandre Minets and Olivier Schiffmann},
+      month={September},
       year={2022},
-      eprint={2209.05429},
+      note={Preprint \href{https://arxiv.org/abs/2209.05429}{arXiv:2209.05429}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2209.05429}, 
 }
 
 @misc{arXiv:2209.02568,
-      title={The $P=W$ conjecture for $\mathrm{GL}_n$}, 
+      title={The {$P=W$} conjecture for {$\mathrm{GL}_n$}}, 
       author={Davesh Maulik and Junliang Shen},
-      year={2024},
+      month={September},
-      eprint={2209.02568},
+      year={2022},
+      note={Preprint \href{https://arxiv.org/abs/2209.02568}{arXiv:2209.02568}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2209.02568}, 
 }
 
 @misc{arXiv:2311.08977,
-      title={A Hodge-theoretic proof of Hwang's theorem on base manifolds of Lagrangian fibrations}, 
+      title={A {H}odge-theoretic proof of {H}wang's theorem on base manifolds of {L}agrangian fibrations}, 
       author={Benjamin Bakker and Christian Schnell},
+      month={November},
       year={2023},
-      eprint={2311.08977},
+      note={Preprint \href{https://arxiv.org/abs/2311.08977}{arXiv:2311.08977}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2311.08977}, 
@@ -200,7 +291,7 @@
       author={Christian Schnell and Ruijie Yang},
       month={September},
       year={2023},
-      eprint={2309.16763},
+      note={Preprint \href{https://arxiv.org/abs/2309.16763}{arXiv:2309.16763}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2309.16763}, 
@@ -242,11 +333,11 @@ MRREVIEWER = {Zhi\ Jiang},
 }
 
 @misc{arXiv:2406.19003,
-      title={Hyperbolicity of generic hypersurfaces of polynomial degree via Green-Griffiths jet differentials}, 
+      title={Hyperbolicity of generic hypersurfaces of polynomial degree via {G}reen-{G}riffiths jet differentials}, 
       author={Benoit Cadorel},
-      year={2024},
       month={June},
-      eprint={2406.19003},
+      year={2024},
+      note={Preprint \href{https://arxiv.org/abs/2406.19003}{arXiv:2406.19003}},
       archivePrefix={arXiv},
       primaryClass={math.AG},
       url={https://arxiv.org/abs/2406.19003},