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183
BAThesis/bibliography.bib
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@ -1,15 +1,3 @@
@Article{Mori2007,
author = {Lapo F. Mori},
journal = {PracTex Journal},
title = {Writing a thesis with LaTex},
year = {2007},
abstract = {This article provides useful tools to write a thesis with LATEX. It analyzes the typical problems that arise while writing a thesis with LaTeX and suggests improved solutions by handling easy packages. Many suggestions can be applied to book and article styles, as well.},
file = {:references/mori.pdf:PDF},
groups = {Writing},
keywords = {Tex},
url = {https://tug.org/pracjourn/2008-1/mori/mori.pdf},
}
@Misc{Biquard2008,
author = {Biquard, Oliver and Höring, Andreas},
month = dec,
@ -18,96 +6,6 @@
comment = {The aim of these lecture notes is to give an introduction to analytic geometry, that is the geometry of complex manifolds, with a focus on the Hodge theory of compact Kähler manifolds. The text comes in two parts that correspond to the distribution of the lectures between the two authors:
- the first part, by Olivier Biquard, is an introduction to Hodge theory, and more generally to the analysis of elliptic operators on compact manifolds.
- the second part, by Andreas Höring, starts with an introduction to complex manifolds and the objects (differential forms, cohomology theories, connections...) naturally attached to them. In Section 4, the analytic results established in the first part are used to prove the existence of the Hodge decomposition on compact Kähler manifolds. Finally in Section 5 we prove the Kodaira vanishing and embedding theorems which establish the link with complex algebraic geometry.},
file = {:references/biquard-höring.pdf:PDF},
groups = {hodge-theory},
ranking = {rank4},
}
@Book{Beauville1996,
author = {Beauville, Arnaud},
publisher = {Cambridge University Press},
title = {Complex algebraic surfaces},
year = {1996},
edition = {2},
isbn = {0521495105},
file = {:references/beauville.pdf:PDF},
groups = {Algebraic Geometry},
ranking = {rank4},
}
@Misc{Sheagren2018,
author = {Calder Sheagren},
note = {Found as a lecturenote online see timestamp for date},
title = {Introduction to Hodge Theory},
year = {2018},
abstract = {We introduce real and complex Hodge theory to study topological invariants using harmonic analysis. To do so, we review Riemannian and complex geometry, intro- duce de Rham cohomology, and give the basic theorems of real and complex Hodge theory. To conclude, we present an application of the complex Hodge decomposition for K ähler manifolds to topology by working out the example of the 2n-torus T2n = Cn/Z2n.},
file = {:references/sheagren.pdf:PDF},
groups = {Hodge Theory},
ranking = {rank4},
relevance = {relevant},
timestamp = {2023-03-23},
url = {http://math.uchicago.edu/~may/REU2018/REUPapers/Sheagren.pdf},
}
@Misc{Park2018,
author = {Peter S. Park},
month = mar,
title = {Hodge Theory},
year = {2018},
abstract = {This exposition of Hodge theory is a slightly retooled version of the author’s Harvard minor thesis, advised by Professor Joe Harris.},
file = {:references/peterspark.pdf:PDF},
groups = {Hodge Theory},
ranking = {rank2},
url = {https://scholar.harvard.edu/files/pspark/files/harvardminorthesis.pdf},
}
@Article{Filippini2014,
author = {Filippini, Sara Angela and Ruddat, Helge and Thompson, Alan},
journal = {Calabi-Yau Varieties: Arithmetic, Geometry and Physics, Fields Inst. Monogr., vol. 34, Springer, 2015, pp. 83-130},
title = {An Introduction to Hodge Structures},
year = {2014},
month = dec,
pages = {83--130},
abstract = {We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kahler manifolds to the families of Hodge structures defined on their cohomology, and discuss its properties. This will lead us to the more general definition of a variation of Hodge structure and the Gauss-Manin connection. We then review the basics about mixed Hodge structures with a view towards degenerations of Hodge structures; including the canonical extension of a vector bundle with connection, Schmid's limiting mixed Hodge structure and Steenbrink's work in the geometric setting. Finally, we give an outlook about Hodge theory in the Gross-Siebert program.},
archiveprefix = {arXiv},
booktitle = {Calabi-Yau Varieties: Arithmetic, Geometry and Physics},
copyright = {arXiv.org perpetual, non-exclusive license},
doi = {10.1007/978-1-4939-2830-9_4},
eprint = {1412.8499},
file = {:http\://arxiv.org/pdf/1412.8499v2:PDF},
groups = {Hodge Theory},
keywords = {Algebraic Geometry (math.AG), FOS: Mathematics, 14C30},
primaryclass = {math.AG},
publisher = {Springer New York},
ranking = {rank3},
}
@Misc{Schwachhoefer20072008,
author = {Viktoria Vilenska},
howpublished = {Homepage of University},
note = {This is a lecture note found online. See timestamp for date.},
title = {Seminar über Kählermannigfaltigkeiten},
year = {2007-2008},
comment = {DO NOT USE:
http://www.mathematik.tu-dortmund.de/~lschwach/WS07/Kaehler-Seminar/},
file = {:references/schwachhöfer.pdf:PDF},
groups = {Hodge Theory},
ranking = {rank1},
timestamp = {2023-03-23},
url = {http://www.mathematik.tu-dortmund.de/~lschwach/WS07/Kaehler-Seminar/Hodge_Theorie.pdf},
}
@Misc{Koch2007,
author = {Artanc Kayacelebi and Jan-Christopher Koch},
howpublished = {Online},
month = dec,
title = {Fast komplexe Mannigfaltigkeiten und Vektorbündel},
year = {2007},
comment = {Do Not Use
There are some usefull definitions of E^(p,q) type differential forms and something about the complexification of the tangent space.},
file = {:references/Koch.pdf:PDF},
ranking = {rank1},
url = {http://www.mathematik.tu-dortmund.de/~lschwach/WS07/Kaehler-Seminar/Fast-Komplex.pdf},
}
@Book{Lee2012,
@ -119,53 +17,7 @@ There are some usefull definitions of E^(p,q) type differential forms and someth
number = {218},
series = {Graduate Texts in Mathematics},
doi = {10.1007/978-1-4419-9982-5},
file = {:references/lee2012.pdf:PDF},
printed = {printed},
qualityassured = {qualityAssured},
ranking = {rank4},
relevance = {relevant},
}
@Book{Bertin2002,
author = {Jose Bertin and Jean-Pierre Demailly and Luc Illusie and Chris Peters},
publisher = {American Mathematical Society},
title = {Introduction to Hodge theory},
year = {2002},
isbn = {0821820400},
abstract = {Hodge theory is a powerful tool in analytic and algebraic geometry. This book consists of expositions of aspects of modern Hodge theory, with the purpose of providing the nonexpert reader with a clear idea of the current state of the subject. The three main topics are: L2 Hodge theory and vanishing theorems; Hodge theory in characteristic p; and variations of Hodge structures and mirror symmetry. Each section has a detailed introduction and numerous references. Many open problems are also included. The reader should have some familiarity with differential and algebraic geometry, with other prerequisites varying by chapter. The book is suitable as an accompaniment to a second course in algebraic geometry. This is the English translation of a volume previously published as volume 3 in the Panoramas et Synthèses series.},
file = {:references/introduction-to-hodge-theory.pdf:PDF},
groups = {Hodge Theroy},
printed = {printed},
qualityassured = {qualityAssured},
ranking = {rank5},
relevance = {relevant},
timestamp = {2023-03-23},
translator = {James Lewis and Chris Peters},
url = {https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/hodge-ams.pdf},
}
@Misc{Bouchard,
author = {Vincent Bouchard},
howpublished = {As a lecture note on the autors personal webpage},
note = {DO NOT USE!! Good explanation of the Hodge Star},
title = {4.8 Hodge Star},
ranking = {rank1},
url = {https://sites.ualberta.ca/~vbouchar/MATH215/section_hodge.html},
}
@Book{Jost2011,
author = {Jost, Jürgen},
publisher = {Springer-Verlag GmbH},
title = {Riemannian Geometry and Geometric Analysis},
year = {2011},
isbn = {9783642212987},
month = jul,
series = {Universitext},
comment = {Capter 3 is about harmonic forms, L2 and the Laplacian operator. Also there could be something about Kähler Manifolds in Chapter 6.},
ean = {9783642212987},
file = {:references/jost.pdf:PDF},
pagetotal = {611},
url = {https://www.ebook.de/de/product/16844179/juergen_jost_riemannian_geometry_and_geometric_analysis.html},
}
@Book{Voisin2002,
@ -177,20 +29,9 @@ There are some usefull definitions of E^(p,q) type differential forms and someth
number = {76},
series = {Cambridge Studies in Advanced Mathematics},
doi = {10.1017/cbo9780511615344},
priority = {prio1},
ranking = {rank5},
}
@Misc{4704312,
author = {Michael Albanese (https://math.stackexchange.com/users/39599/michael-albanese)},
howpublished = {Mathematics Stack Exchange},
note = {URL:https://math.stackexchange.com/q/4704312 (version: 2023-05-22)},
title = {Dimensions of underlying real spaces and dimensions of complexifications},
year = {2023},
eprint = {https://math.stackexchange.com/q/4704312},
keywords = {Stack Exchange},
url = {https://math.stackexchange.com/q/4704312},
}
@Book{Wells1986,
author = {Wells, Raymond O'Neil},
@ -200,7 +41,6 @@ There are some usefull definitions of E^(p,q) type differential forms and someth
isbn = {9780387904191},
series = {Graduate Texts in Mathematics},
volume = {65},
comment = {Found in mathematical Library of the mathematical institut of the university of freiburg},
pages = {260},
}
@ -212,21 +52,9 @@ There are some usefull definitions of E^(p,q) type differential forms and someth
isbn = {9783540212904},
series = {Universitext},
doi = {10.1007/b137952},
file = {:references/huybrechts.pdf:PDF},
qualityassured = {qualityAssured},
ranking = {rank4},
subtitle = {An Introduction},
}
@Misc{1417853,
author = {user24142 (https://math.stackexchange.com/users/208255/user24142)},
howpublished = {Mathematics Stack Exchange},
note = {URL:https://math.stackexchange.com/q/1417853 (version: 2015-09-02)},
title = {How do you show that conjugate mapping, $ f(z)=\bar {z}$ isn't linear?},
eprint = {https://math.stackexchange.com/q/1417853},
url = {https://math.stackexchange.com/q/1417853},
}
@Book{Spivak1965,
author = {Spivak, Michael},
publisher = {Addison-Wesley},
@ -234,7 +62,6 @@ There are some usefull definitions of E^(p,q) type differential forms and someth
year = {1965},
edition = {1},
isbn = {0805390219},
file = {:references/spivak-calculus-on-manifolds.pdf:PDF},
subtitle = {a modern approach to classical theorems of advanced calculus.},
}
@ -243,7 +70,6 @@ There are some usefull definitions of E^(p,q) type differential forms and someth
publisher = {Citeseer},
title = {Complex analytic and differential geometry},
year = {1997},
file = {:references/demailly.pdf:PDF},
url = {https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=88c41281e6910c945cfa79ef6a70d799d6f3a8b4},
}
@ -256,7 +82,6 @@ There are some usefull definitions of E^(p,q) type differential forms and someth
number = {94},
series = {Graduate Texts in Mathematics},
doi = {10.1007/978-1-4757-1799-0},
file = {:references/Warner1983.pdf:PDF},
}
@Misc{Schnell2012,
@ -264,7 +89,6 @@ There are some usefull definitions of E^(p,q) type differential forms and someth
howpublished = {Lecture notes published online},
title = {Complex manifolds},
year = {2012},
file = {:references/schnell2012.pdf:PDF},
url = {https://www.math.stonybrook.edu/~cschnell/pdf/notes/complex-manifolds.pdf},
}
@ -278,7 +102,6 @@ There are some usefull definitions of E^(p,q) type differential forms and someth
series = {Ergebnisse der Mathematik und ihrer Grenzgebiete / A series of modern surveys in mathematics},
volume = {4},
doi = {10.1007/978-3-642-96754-2},
file = {:references/barth1984.pdf:PDF},
}
@Misc{SEMark,
@ -288,7 +111,3 @@ There are some usefull definitions of E^(p,q) type differential forms and someth
title = {Dual of the complexification is complexification of the dual},
url = {https://math.stackexchange.com/q/4718945},
}
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@Comment{jabref-meta: fileDirectoryLatex-danielrath-MBP-von-Daniel.fritz.box:/Users/danielrath/Documents/Studium/Bachelorarbeit/bachelor-thesis;}

156
LICENSE Normal file
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@ -0,0 +1,156 @@
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Creative Commons public licenses provide a standard set of terms and conditions that creators and other rights holders may use to share original works of authorship and other material subject to copyright and certain other rights specified in the public license below. The following considerations are for informational purposes only, are not exhaustive, and do not form part of our licenses.
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Considerations for the public: By using one of our public licenses, a licensor grants the public permission to use the licensed material under specified terms and conditions. If the licensor’s permission is not necessary for any reason–for example, because of any applicable exception or limitation to copyright–then that use is not regulated by the license. Our licenses grant only permissions under copyright and certain other rights that a licensor has authority to grant. Use of the licensed material may still be restricted for other reasons, including because others have copyright or other rights in the material. A licensor may make special requests, such as asking that all changes be marked or described. Although not required by our licenses, you are encouraged to respect those requests where reasonable. More considerations for the public.
Creative Commons Attribution 4.0 International Public License
By exercising the Licensed Rights (defined below), You accept and agree to be bound by the terms and conditions of this Creative Commons Attribution 4.0 International Public License ("Public License"). To the extent this Public License may be interpreted as a contract, You are granted the Licensed Rights in consideration of Your acceptance of these terms and conditions, and the Licensor grants You such rights in consideration of benefits the Licensor receives from making the Licensed Material available under these terms and conditions.
Section 1 – Definitions.
a. Adapted Material means material subject to Copyright and Similar Rights that is derived from or based upon the Licensed Material and in which the Licensed Material is translated, altered, arranged, transformed, or otherwise modified in a manner requiring permission under the Copyright and Similar Rights held by the Licensor. For purposes of this Public License, where the Licensed Material is a musical work, performance, or sound recording, Adapted Material is always produced where the Licensed Material is synched in timed relation with a moving image.
b. Adapter's License means the license You apply to Your Copyright and Similar Rights in Your contributions to Adapted Material in accordance with the terms and conditions of this Public License.
c. Copyright and Similar Rights means copyright and/or similar rights closely related to copyright including, without limitation, performance, broadcast, sound recording, and Sui Generis Database Rights, without regard to how the rights are labeled or categorized. For purposes of this Public License, the rights specified in Section 2(b)(1)-(2) are not Copyright and Similar Rights.
d. Effective Technological Measures means those measures that, in the absence of proper authority, may not be circumvented under laws fulfilling obligations under Article 11 of the WIPO Copyright Treaty adopted on December 20, 1996, and/or similar international agreements.
e. Exceptions and Limitations means fair use, fair dealing, and/or any other exception or limitation to Copyright and Similar Rights that applies to Your use of the Licensed Material.
f. Licensed Material means the artistic or literary work, database, or other material to which the Licensor applied this Public License.
g. Licensed Rights means the rights granted to You subject to the terms and conditions of this Public License, which are limited to all Copyright and Similar Rights that apply to Your use of the Licensed Material and that the Licensor has authority to license.
h. Licensor means the individual(s) or entity(ies) granting rights under this Public License.
i. Share means to provide material to the public by any means or process that requires permission under the Licensed Rights, such as reproduction, public display, public performance, distribution, dissemination, communication, or importation, and to make material available to the public including in ways that members of the public may access the material from a place and at a time individually chosen by them.
j. Sui Generis Database Rights means rights other than copyright resulting from Directive 96/9/EC of the European Parliament and of the Council of 11 March 1996 on the legal protection of databases, as amended and/or succeeded, as well as other essentially equivalent rights anywhere in the world.
k. You means the individual or entity exercising the Licensed Rights under this Public License. Your has a corresponding meaning.
Section 2 – Scope.
a. License grant.
1. Subject to the terms and conditions of this Public License, the Licensor hereby grants You a worldwide, royalty-free, non-sublicensable, non-exclusive, irrevocable license to exercise the Licensed Rights in the Licensed Material to:
A. reproduce and Share the Licensed Material, in whole or in part; and
B. produce, reproduce, and Share Adapted Material.
2. Exceptions and Limitations. For the avoidance of doubt, where Exceptions and Limitations apply to Your use, this Public License does not apply, and You do not need to comply with its terms and conditions.
3. Term. The term of this Public License is specified in Section 6(a).
4. Media and formats; technical modifications allowed. The Licensor authorizes You to exercise the Licensed Rights in all media and formats whether now known or hereafter created, and to make technical modifications necessary to do so. The Licensor waives and/or agrees not to assert any right or authority to forbid You from making technical modifications necessary to exercise the Licensed Rights, including technical modifications necessary to circumvent Effective Technological Measures. For purposes of this Public License, simply making modifications authorized by this Section 2(a)(4) never produces Adapted Material.
5. Downstream recipients.
A. Offer from the Licensor – Licensed Material. Every recipient of the Licensed Material automatically receives an offer from the Licensor to exercise the Licensed Rights under the terms and conditions of this Public License.
B. No downstream restrictions. You may not offer or impose any additional or different terms or conditions on, or apply any Effective Technological Measures to, the Licensed Material if doing so restricts exercise of the Licensed Rights by any recipient of the Licensed Material.
6. No endorsement. Nothing in this Public License constitutes or may be construed as permission to assert or imply that You are, or that Your use of the Licensed Material is, connected with, or sponsored, endorsed, or granted official status by, the Licensor or others designated to receive attribution as provided in Section 3(a)(1)(A)(i).
b. Other rights.
1. Moral rights, such as the right of integrity, are not licensed under this Public License, nor are publicity, privacy, and/or other similar personality rights; however, to the extent possible, the Licensor waives and/or agrees not to assert any such rights held by the Licensor to the limited extent necessary to allow You to exercise the Licensed Rights, but not otherwise.
2. Patent and trademark rights are not licensed under this Public License.
3. To the extent possible, the Licensor waives any right to collect royalties from You for the exercise of the Licensed Rights, whether directly or through a collecting society under any voluntary or waivable statutory or compulsory licensing scheme. In all other cases the Licensor expressly reserves any right to collect such royalties.
Section 3 – License Conditions.
Your exercise of the Licensed Rights is expressly made subject to the following conditions.
a. Attribution.
1. If You Share the Licensed Material (including in modified form), You must:
A. retain the following if it is supplied by the Licensor with the Licensed Material:
i. identification of the creator(s) of the Licensed Material and any others designated to receive attribution, in any reasonable manner requested by the Licensor (including by pseudonym if designated);
ii. a copyright notice;
iii. a notice that refers to this Public License;
iv. a notice that refers to the disclaimer of warranties;
v. a URI or hyperlink to the Licensed Material to the extent reasonably practicable;
B. indicate if You modified the Licensed Material and retain an indication of any previous modifications; and
C. indicate the Licensed Material is licensed under this Public License, and include the text of, or the URI or hyperlink to, this Public License.
2. You may satisfy the conditions in Section 3(a)(1) in any reasonable manner based on the medium, means, and context in which You Share the Licensed Material. For example, it may be reasonable to satisfy the conditions by providing a URI or hyperlink to a resource that includes the required information.
3. If requested by the Licensor, You must remove any of the information required by Section 3(a)(1)(A) to the extent reasonably practicable.
4. If You Share Adapted Material You produce, the Adapter's License You apply must not prevent recipients of the Adapted Material from complying with this Public License.
Section 4 – Sui Generis Database Rights.
Where the Licensed Rights include Sui Generis Database Rights that apply to Your use of the Licensed Material:
a. for the avoidance of doubt, Section 2(a)(1) grants You the right to extract, reuse, reproduce, and Share all or a substantial portion of the contents of the database;
b. if You include all or a substantial portion of the database contents in a database in which You have Sui Generis Database Rights, then the database in which You have Sui Generis Database Rights (but not its individual contents) is Adapted Material; and
c. You must comply with the conditions in Section 3(a) if You Share all or a substantial portion of the contents of the database.
For the avoidance of doubt, this Section 4 supplements and does not replace Your obligations under this Public License where the Licensed Rights include other Copyright and Similar Rights.
Section 5 – Disclaimer of Warranties and Limitation of Liability.
a. Unless otherwise separately undertaken by the Licensor, to the extent possible, the Licensor offers the Licensed Material as-is and as-available, and makes no representations or warranties of any kind concerning the Licensed Material, whether express, implied, statutory, or other. This includes, without limitation, warranties of title, merchantability, fitness for a particular purpose, non-infringement, absence of latent or other defects, accuracy, or the presence or absence of errors, whether or not known or discoverable. Where disclaimers of warranties are not allowed in full or in part, this disclaimer may not apply to You.
b. To the extent possible, in no event will the Licensor be liable to You on any legal theory (including, without limitation, negligence) or otherwise for any direct, special, indirect, incidental, consequential, punitive, exemplary, or other losses, costs, expenses, or damages arising out of this Public License or use of the Licensed Material, even if the Licensor has been advised of the possibility of such losses, costs, expenses, or damages. Where a limitation of liability is not allowed in full or in part, this limitation may not apply to You.
c. The disclaimer of warranties and limitation of liability provided above shall be interpreted in a manner that, to the extent possible, most closely approximates an absolute disclaimer and waiver of all liability.
Section 6 – Term and Termination.
a. This Public License applies for the term of the Copyright and Similar Rights licensed here. However, if You fail to comply with this Public License, then Your rights under this Public License terminate automatically.
b. Where Your right to use the Licensed Material has terminated under Section 6(a), it reinstates:
1. automatically as of the date the violation is cured, provided it is cured within 30 days of Your discovery of the violation; or
2. upon express reinstatement by the Licensor.
c. For the avoidance of doubt, this Section 6(b) does not affect any right the Licensor may have to seek remedies for Your violations of this Public License.
d. For the avoidance of doubt, the Licensor may also offer the Licensed Material under separate terms or conditions or stop distributing the Licensed Material at any time; however, doing so will not terminate this Public License.
e. Sections 1, 5, 6, 7, and 8 survive termination of this Public License.
Section 7 – Other Terms and Conditions.
a. The Licensor shall not be bound by any additional or different terms or conditions communicated by You unless expressly agreed.
b. Any arrangements, understandings, or agreements regarding the Licensed Material not stated herein are separate from and independent of the terms and conditions of this Public License.
Section 8 – Interpretation.
a. For the avoidance of doubt, this Public License does not, and shall not be interpreted to, reduce, limit, restrict, or impose conditions on any use of the Licensed Material that could lawfully be made without permission under this Public License.
b. To the extent possible, if any provision of this Public License is deemed unenforceable, it shall be automatically reformed to the minimum extent necessary to make it enforceable. If the provision cannot be reformed, it shall be severed from this Public License without affecting the enforceability of the remaining terms and conditions.
c. No term or condition of this Public License will be waived and no failure to comply consented to unless expressly agreed to by the Licensor.
d. Nothing in this Public License constitutes or may be interpreted as a limitation upon, or waiver of, any privileges and immunities that apply to the Licensor or You, including from the legal processes of any jurisdiction or authority.
Creative Commons is not a party to its public licenses. Notwithstanding, Creative Commons may elect to apply one of its public licenses to material it publishes and in those instances will be considered the “Licensor.” Except for the limited purpose of indicating that material is shared under a Creative Commons public license or as otherwise permitted by the Creative Commons policies published at creativecommons.org/policies, Creative Commons does not authorize the use of the trademark “Creative Commons” or any other trademark or logo of Creative Commons without its prior written consent including, without limitation, in connection with any unauthorized modifications to any of its public licenses or any other arrangements, understandings, or agreements concerning use of licensed material. For the avoidance of doubt, this paragraph does not form part of the public licenses.
Creative Commons may be contacted at creativecommons.org.