K3 Surfaces And Their Moduli

Author : Carel Faber,Gavril Farkas,Gerard van der Geer
Publisher : Birkhäuser
Page : 399 pages
File Size : 46,8 Mb
Release : 2016-04-22
Category : Mathematics
ISBN : 9783319299594

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K3 Surfaces and Their Moduli by Carel Faber,Gavril Farkas,Gerard van der Geer Pdf

This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties,” which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics. K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both mathematicians and theoretical physicists. Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significant impetus due to recent breakthroughs on the Tate conjecture, the study of stability conditions and derived categories, and links with mirror symmetry and string theory. At the same time, the theory of irreducible holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has become a mainstream topic in algebraic geometry. Contributors: S. Boissière, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M. Nieper-Wisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.

Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 499 pages
File Size : 54,8 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9781107153042

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Lectures on K3 Surfaces by Daniel Huybrechts Pdf

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

Author : Francesco Scattone
Publisher : American Mathematical Soc.
Page : 86 pages
File Size : 42,7 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821824375

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On the Compactification of Moduli Spaces for Algebraic $K3$ Surfaces by Francesco Scattone Pdf

Author : Daniel Huybrechts,Manfred Lehn
Publisher : Cambridge University Press
Page : 345 pages
File Size : 50,7 Mb
Release : 2010-05-27
Category : Mathematics
ISBN : 9781139485821

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The Geometry of Moduli Spaces of Sheaves by Daniel Huybrechts,Manfred Lehn Pdf

This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Author : SHIGEYUKI. KONDO
Publisher : Unknown
Page : 128 pages
File Size : 51,5 Mb
Release : 2020
Category : Electronic
ISBN : 3037192089

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K3 SURFACES. by SHIGEYUKI. KONDO Pdf

Author : Radu Laza,Matthias Schütt,Noriko Yui
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 44,5 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781461464037

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Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds by Radu Laza,Matthias Schütt,Noriko Yui Pdf

In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.

Author : F. Cossec,Dolgachev
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461236962

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Enriques Surfaces I by F. Cossec,Dolgachev Pdf

This is the first of two volumes representing the current state of knowledge about Enriques surfaces which occupy one of the classes in the classification of algebraic surfaces. Recent improvements in our understanding of algebraic surfaces over fields of positive characteristic allowed us to approach the subject from a completely geometric point of view although heavily relying on algebraic methods. Some of the techniques presented in this book can be applied to the study of algebraic surfaces of other types. We hope that it will make this book of particular interest to a wider range of research mathematicians and graduate students. Acknowledgements. The undertaking of this project was made possible by the support of several institutions. Our mutual cooperation began at the University of Warwick and the Max Planck Institute of Mathematics in 1982/83. Most of the work in this volume was done during the visit of the first author at the University of Michigan in 1984-1986. The second author was supported during all these years by grants from the National Science Foundation.

Author : Kunihiko Kodaira,W. L. Jr Baily,T. Shioda
Publisher : CUP Archive
Page : 424 pages
File Size : 52,8 Mb
Release : 1977
Category : Mathematics
ISBN : 0521217776

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Complex Analysis and Algebraic Geometry by Kunihiko Kodaira,W. L. Jr Baily,T. Shioda Pdf

The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.

Author : Leticia Brambila,Oscar García-Prada,Peter Newstead,Richard P. Thomas
Publisher : Cambridge University Press
Page : 347 pages
File Size : 48,7 Mb
Release : 2014-03-13
Category : Mathematics
ISBN : 9781107636385

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Moduli Spaces by Leticia Brambila,Oscar García-Prada,Peter Newstead,Richard P. Thomas Pdf

A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

Author : Paul Hacking,Radu Laza,Dragos Oprea
Publisher : Birkhäuser
Page : 135 pages
File Size : 53,6 Mb
Release : 2016-02-04
Category : Mathematics
ISBN : 9783034809214

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Compactifying Moduli Spaces by Paul Hacking,Radu Laza,Dragos Oprea Pdf

This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps. Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.

Author : Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447148630

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Symmetries, Integrable Systems and Representations by Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy Pdf

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Author : Dan Abramovich
Publisher : American Mathematical Soc.
Page : 506 pages
File Size : 50,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847022

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Algebraic Geometry by Dan Abramovich Pdf

This volume contains research and expository papers by some of the speakers at the 2005 AMS Summer Institute on Algebraic Geometry. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties.

Author : Jean-Benoît Bost,Helmut Hofer,François Labourie,Yves Le Jan,Xiaonan Ma,Weiping Zhang
Publisher : Birkhäuser
Page : 361 pages
File Size : 47,9 Mb
Release : 2017-04-26
Category : Mathematics
ISBN : 9783319496382

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Geometry, Analysis and Probability by Jean-Benoît Bost,Helmut Hofer,François Labourie,Yves Le Jan,Xiaonan Ma,Weiping Zhang Pdf

This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.

Author : Gavril Farkas,Gerard van der Geer,Mingmin Shen,Lenny Taelman
Publisher : Springer Nature
Page : 433 pages
File Size : 48,8 Mb
Release : 2021-10-19
Category : Mathematics
ISBN : 9783030754211

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Rationality of Varieties by Gavril Farkas,Gerard van der Geer,Mingmin Shen,Lenny Taelman Pdf

This book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces and birational invariants of group actions on varieties, contributed by the foremost experts in their fields. The question of whether an algebraic variety can be parametrized by rational functions of as many variables as its dimension has a long history and played an important role in the history of algebraic geometry. Recent developments in algebraic geometry have made this question again a focal point of research and formed the impetus to organize a conference in the series of conferences on the island of Schiermonnikoog. The book follows in the tradition of earlier volumes, which originated from conferences on the islands Texel and Schiermonnikoog.

Author : Markus Zowislok
Publisher : Sudwestdeutscher Verlag Fur Hochschulschriften AG
Page : 120 pages
File Size : 47,5 Mb
Release : 2010
Category : Electronic
ISBN : 3838119088

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On Moduli Spaces of Semistable Sheaves on K3 Surfaces by Markus Zowislok Pdf

A big challenge in symplectic geometry is the search for irreducible symplectic manifolds. After O'Grady constructed striking examples out of singular moduli spaces of sheaves on projective abelian and K3 surfaces for special nonprimitive Mukai vectors v with v.v=8, Kaledin, Lehn and Sorger proved that for all nonprimitive Mukai vectors v with v.v>8 the moduli space is not symplectically resolvable if the ample divisor is general. In this thesis we investigate the remaining cases of moduli spaces of semistable sheaves on projective K3 surfaces - the cases of Mukai vector (0, c,0) as well as moduli spaces for nongeneral ample divisors - with regard to the possible construction of new examples of projective irreducible symplectic manifolds. We establish a connection to the already investigated moduli spaces or generalisations thereof, and we are able to extend the known results to all of the open remaining cases for rank 0 and many of those for positive rank. In particular, we can exclude for these cases the existence of new examples of projective irreducible symplectic manifolds lying birationally over components of the moduli space.