295 lines
13 KiB
BibTeX
295 lines
13 KiB
BibTeX
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@Article{Mori2007,
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author = {Lapo F. Mori},
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journal = {PracTex Journal},
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title = {Writing a thesis with LaTex},
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year = {2007},
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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.},
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file = {:references/mori.pdf:PDF},
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groups = {Writing},
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keywords = {Tex},
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url = {https://tug.org/pracjourn/2008-1/mori/mori.pdf},
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}
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@Misc{Biquard2008,
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author = {Biquard, Oliver and Höring, Andreas},
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month = dec,
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title = {Kähler Geometry and Hodge Theory},
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year = {2008},
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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:
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- the first part, by Olivier Biquard, is an introduction to Hodge theory, and more generally to the analysis of elliptic operators on compact manifolds.
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- 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.},
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file = {:references/biquard-höring.pdf:PDF},
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groups = {hodge-theory},
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ranking = {rank4},
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}
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@Book{Beauville1996,
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author = {Beauville, Arnaud},
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publisher = {Cambridge University Press},
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title = {Complex algebraic surfaces},
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year = {1996},
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edition = {2},
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isbn = {0521495105},
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file = {:references/beauville.pdf:PDF},
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groups = {Algebraic Geometry},
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ranking = {rank4},
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}
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@Misc{Sheagren2018,
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author = {Calder Sheagren},
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note = {Found as a lecturenote online see timestamp for date},
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title = {Introduction to Hodge Theory},
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year = {2018},
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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.},
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file = {:references/sheagren.pdf:PDF},
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groups = {Hodge Theory},
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ranking = {rank4},
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relevance = {relevant},
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timestamp = {2023-03-23},
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url = {http://math.uchicago.edu/~may/REU2018/REUPapers/Sheagren.pdf},
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}
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@Misc{Park2018,
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author = {Peter S. Park},
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month = mar,
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title = {Hodge Theory},
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year = {2018},
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abstract = {This exposition of Hodge theory is a slightly retooled version of the author’s Harvard minor thesis, advised by Professor Joe Harris.},
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file = {:references/peterspark.pdf:PDF},
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groups = {Hodge Theory},
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ranking = {rank2},
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url = {https://scholar.harvard.edu/files/pspark/files/harvardminorthesis.pdf},
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}
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@Article{Filippini2014,
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author = {Filippini, Sara Angela and Ruddat, Helge and Thompson, Alan},
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journal = {Calabi-Yau Varieties: Arithmetic, Geometry and Physics, Fields Inst. Monogr., vol. 34, Springer, 2015, pp. 83-130},
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title = {An Introduction to Hodge Structures},
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year = {2014},
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month = dec,
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pages = {83--130},
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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.},
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archiveprefix = {arXiv},
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booktitle = {Calabi-Yau Varieties: Arithmetic, Geometry and Physics},
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copyright = {arXiv.org perpetual, non-exclusive license},
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doi = {10.1007/978-1-4939-2830-9_4},
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eprint = {1412.8499},
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file = {:http\://arxiv.org/pdf/1412.8499v2:PDF},
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groups = {Hodge Theory},
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keywords = {Algebraic Geometry (math.AG), FOS: Mathematics, 14C30},
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primaryclass = {math.AG},
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publisher = {Springer New York},
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ranking = {rank3},
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}
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@Misc{Schwachhoefer20072008,
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author = {Viktoria Vilenska},
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howpublished = {Homepage of University},
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note = {This is a lecture note found online. See timestamp for date.},
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title = {Seminar über Kählermannigfaltigkeiten},
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year = {2007-2008},
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comment = {DO NOT USE:
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http://www.mathematik.tu-dortmund.de/~lschwach/WS07/Kaehler-Seminar/},
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file = {:references/schwachhöfer.pdf:PDF},
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groups = {Hodge Theory},
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ranking = {rank1},
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timestamp = {2023-03-23},
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url = {http://www.mathematik.tu-dortmund.de/~lschwach/WS07/Kaehler-Seminar/Hodge_Theorie.pdf},
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}
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@Misc{Koch2007,
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author = {Artanc Kayacelebi and Jan-Christopher Koch},
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howpublished = {Online},
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month = dec,
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title = {Fast komplexe Mannigfaltigkeiten und Vektorbündel},
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year = {2007},
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comment = {Do Not Use
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There are some usefull definitions of E^(p,q) type differential forms and something about the complexification of the tangent space.},
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file = {:references/Koch.pdf:PDF},
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ranking = {rank1},
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url = {http://www.mathematik.tu-dortmund.de/~lschwach/WS07/Kaehler-Seminar/Fast-Komplex.pdf},
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}
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@Book{Lee2012,
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author = {Lee, John M.},
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publisher = {Springer New York},
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title = {Introduction to Smooth Manifolds},
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year = {2012},
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edition = {2},
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number = {218},
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series = {Graduate Texts in Mathematics},
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doi = {10.1007/978-1-4419-9982-5},
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file = {:references/lee2012.pdf:PDF},
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printed = {printed},
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qualityassured = {qualityAssured},
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ranking = {rank4},
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relevance = {relevant},
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}
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@Book{Bertin2002,
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author = {Jose Bertin and Jean-Pierre Demailly and Luc Illusie and Chris Peters},
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publisher = {American Mathematical Society},
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title = {Introduction to Hodge theory},
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year = {2002},
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isbn = {0821820400},
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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.},
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file = {:references/introduction-to-hodge-theory.pdf:PDF},
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groups = {Hodge Theroy},
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printed = {printed},
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qualityassured = {qualityAssured},
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ranking = {rank5},
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relevance = {relevant},
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timestamp = {2023-03-23},
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translator = {James Lewis and Chris Peters},
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url = {https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/hodge-ams.pdf},
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}
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@Misc{Bouchard,
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author = {Vincent Bouchard},
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howpublished = {As a lecture note on the autors personal webpage},
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note = {DO NOT USE!! Good explanation of the Hodge Star},
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title = {4.8 Hodge Star},
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ranking = {rank1},
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url = {https://sites.ualberta.ca/~vbouchar/MATH215/section_hodge.html},
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}
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@Book{Jost2011,
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author = {Jost, Jürgen},
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publisher = {Springer-Verlag GmbH},
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title = {Riemannian Geometry and Geometric Analysis},
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year = {2011},
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isbn = {9783642212987},
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month = jul,
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series = {Universitext},
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comment = {Capter 3 is about harmonic forms, L2 and the Laplacian operator. Also there could be something about Kähler Manifolds in Chapter 6.},
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ean = {9783642212987},
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file = {:references/jost.pdf:PDF},
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pagetotal = {611},
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url = {https://www.ebook.de/de/product/16844179/juergen_jost_riemannian_geometry_and_geometric_analysis.html},
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}
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@Book{Voisin2002,
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author = {Voisin, Claire},
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publisher = {Cambridge University Press},
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title = {Hodge Theory and Complex Algebraic Geometry I},
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year = {2002},
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isbn = {9780521718011},
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number = {76},
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series = {Cambridge Studies in Advanced Mathematics},
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doi = {10.1017/cbo9780511615344},
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priority = {prio1},
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ranking = {rank5},
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}
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@Misc{4704312,
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author = {Michael Albanese (https://math.stackexchange.com/users/39599/michael-albanese)},
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howpublished = {Mathematics Stack Exchange},
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note = {URL:https://math.stackexchange.com/q/4704312 (version: 2023-05-22)},
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title = {Dimensions of underlying real spaces and dimensions of complexifications},
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year = {2023},
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eprint = {https://math.stackexchange.com/q/4704312},
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keywords = {Stack Exchange},
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url = {https://math.stackexchange.com/q/4704312},
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}
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@Book{Wells1986,
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author = {Wells, Raymond O'Neil},
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publisher = {Springer},
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title = {Differential Analysis on Complex Manifolds},
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year = {1986},
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isbn = {9780387904191},
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series = {Graduate Texts in Mathematics},
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volume = {65},
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comment = {Found in mathematical Library of the mathematical institut of the university of freiburg},
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pages = {260},
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}
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@Book{Huybrechts2004,
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author = {Huybrechts, Daniel},
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publisher = {Springer},
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title = {Complex Geometry},
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year = {2004},
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isbn = {9783540212904},
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series = {Universitext},
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doi = {10.1007/b137952},
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file = {:references/huybrechts.pdf:PDF},
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qualityassured = {qualityAssured},
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ranking = {rank4},
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subtitle = {An Introduction},
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}
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@Misc{1417853,
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author = {user24142 (https://math.stackexchange.com/users/208255/user24142)},
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howpublished = {Mathematics Stack Exchange},
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note = {URL:https://math.stackexchange.com/q/1417853 (version: 2015-09-02)},
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title = {How do you show that conjugate mapping, $ f(z)=\bar {z}$ isn't linear?},
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eprint = {https://math.stackexchange.com/q/1417853},
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url = {https://math.stackexchange.com/q/1417853},
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}
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@Book{Spivak1965,
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author = {Spivak, Michael},
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publisher = {Addison-Wesley},
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title = {Calculus on manifolds},
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year = {1965},
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edition = {1},
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isbn = {0805390219},
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file = {:references/spivak-calculus-on-manifolds.pdf:PDF},
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subtitle = {a modern approach to classical theorems of advanced calculus.},
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}
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@Book{Demailly1997,
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author = {Demailly, Jean-Pierre},
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publisher = {Citeseer},
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title = {Complex analytic and differential geometry},
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year = {1997},
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file = {:references/demailly.pdf:PDF},
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url = {https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=88c41281e6910c945cfa79ef6a70d799d6f3a8b4},
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}
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@Book{Warner1983,
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author = {Frank W. Warner},
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publisher = {Springer New York},
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title = {Foundations of Differentiable Manifolds and Lie Groups},
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year = {1983},
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edition = {1},
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number = {94},
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series = {Graduate Texts in Mathematics},
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doi = {10.1007/978-1-4757-1799-0},
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file = {:references/Warner1983.pdf:PDF},
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}
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@Misc{Schnell2012,
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author = {Christian Schnell},
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howpublished = {Lecture notes published online},
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title = {Complex manifolds},
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year = {2012},
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file = {:references/schnell2012.pdf:PDF},
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url = {https://www.math.stonybrook.edu/~cschnell/pdf/notes/complex-manifolds.pdf},
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}
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@Book{Barth1984,
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author = {W. Barth and C. Peters and A. Ven},
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publisher = {Springer},
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title = {Compact Complex Surfaces},
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year = {1984},
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edition = {1},
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number = {3},
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series = {Ergebnisse der Mathematik und ihrer Grenzgebiete / A series of modern surveys in mathematics},
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volume = {4},
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doi = {10.1007/978-3-642-96754-2},
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file = {:references/barth1984.pdf:PDF},
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}
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@Misc{SEMark,
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author = {Mark},
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howpublished = {Mathematics Stack Exchange},
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note = {URL:https://math.stackexchange.com/q/4718945 (version: 2023-06-14)},
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title = {Dual of the complexification is complexification of the dual},
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url = {https://math.stackexchange.com/q/4718945},
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}
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@Comment{jabref-meta: databaseType:bibtex;}
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@Comment{jabref-meta: fileDirectoryLatex-danielrath-MBP-von-Daniel.fritz.box:/Users/danielrath/Documents/Studium/Bachelorarbeit/bachelor-thesis;}
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