Compact Moduli Spaces And Vector Bundles

Author : Valery Alexeev
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 44,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821868997

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Compact Moduli Spaces and Vector Bundles by Valery Alexeev Pdf

This book contains the proceedings of the conference on Compact Moduli and Vector Bundles, held from October 21-24, 2010, at the University of Georgia. This book is a mix of survey papers and original research articles on two related subjects: Compact Moduli spaces of algebraic varieties, including of higher-dimensional stable varieties and pairs, and Vector Bundles on such compact moduli spaces, including the conformal block bundles. These bundles originated in the 1970s in physics; the celebrated Verlinde formula computes their ranks. Among the surveys are those that examine compact moduli spaces of surfaces of general type and others that concern the GIT constructions of log canonical models of moduli of stable curves. The original research articles include, among others, papers on a formula for the Chern classes of conformal classes of conformal block bundles on the moduli spaces of stable curves, on Looijenga's conjectures, on algebraic and tropical Brill-Noether theory, on Green's conjecture, on rigid curves on moduli of curves, and on Steiner surfaces.

Author : Valery Alexeev
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 44,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821889541

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Compact Moduli Spaces and Vector Bundles by Valery Alexeev Pdf

Author : Steve Bradlow
Publisher : Cambridge University Press
Page : 516 pages
File Size : 41,8 Mb
Release : 2009-05-21
Category : Mathematics
ISBN : 9780521734714

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Moduli Spaces and Vector Bundles by Steve Bradlow Pdf

Coverage includes foundational material as well as current research, authored by top specialists within their fields.

Author : Paul Hacking,Radu Laza,Dragos Oprea
Publisher : Birkhäuser
Page : 135 pages
File Size : 43,8 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 : Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov
Publisher : Springer
Page : 231 pages
File Size : 54,7 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9783030029432

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Algebraic Curves by Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov Pdf

This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework

Author : Vasile Brinzanescu
Publisher : Springer
Page : 175 pages
File Size : 42,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540498452

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Holomorphic Vector Bundles over Compact Complex Surfaces by Vasile Brinzanescu Pdf

The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector bundles and stability with respect to a Gauduchon metric, are considered. The reader requires a grounding in geometry at graduate student level. The book will be of interest to graduate students and researchers in complex, algebraic and differential geometry.

Author : Peter Beier Gothen,Margarida Melo (Mathematician),Montserrat Teixidor i Bigas
Publisher : Unknown
Page : 0 pages
File Size : 53,5 Mb
Release : 2024
Category : Moduli theory
ISBN : 1470472961

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Moduli Spaces and Vector Bundles by Peter Beier Gothen,Margarida Melo (Mathematician),Montserrat Teixidor i Bigas Pdf

Author : Cristian Anghel,Iustin Coandă,Nicolae Manolache
Publisher : American Mathematical Soc.
Page : 107 pages
File Size : 52,9 Mb
Release : 2018-05-29
Category : Chern classes
ISBN : 9781470428389

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Globally Generated Vector Bundles with Small C1 on Projective Spaces by Cristian Anghel,Iustin Coandă,Nicolae Manolache Pdf

Author : David Ellwood,Emma Previato
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 49,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852057

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Grassmannians, Moduli Spaces and Vector Bundles by David Ellwood,Emma Previato Pdf

This collection of cutting-edge articles on vector bundles and related topics originated from a CMI workshop, held in October 2006, that brought together a community indebted to the pioneering work of P. E. Newstead, visiting the United States for the first time since the 1960s. Moduli spaces of vector bundles were then in their infancy, but are now, as demonstrated by this volume, a powerful tool in symplectic geometry, number theory, mathematical physics, and algebraic geometry. In fact, the impetus for this volume was to offer a sample of the vital convergence of techniques and fundamental progress, taking place in moduli spaces at the outset of the twenty-first century. This volume contains contributions by J. E. Andersen and N. L. Gammelgaard (Hitchin's projectively flat connection and Toeplitz operators), M. Aprodu and G. Farkas (moduli spaces), D. Arcara and A. Bertram (stability in higher dimension), L. Jeffrey (intersection cohomology), J. Kamnitzer (Langlands program), M. Lieblich (arithmetic aspects), P. E. Newstead (coherent systems), G. Pareschi and M. Popa (linear series on Abelian varieties), and M. Teixidor i Bigas (bundles over reducible curves). These articles do require a working knowledge of algebraic geometry, symplectic geometry and functional analysis, but should appeal to practitioners in a diversity of fields. No specialization should be necessary to appreciate the contributions, or possibly to be stimulated to work in the various directions opened by these path-blazing ideas; to mention a few, the Langlands program, stability criteria for vector bundles over surfaces and threefolds, linear series over abelian varieties and Brauer groups in relation to arithmetic properties of moduli spaces.

Author : Masaki Maruyama
Publisher : CRC Press
Page : 324 pages
File Size : 47,8 Mb
Release : 1996-04-23
Category : Mathematics
ISBN : 0824797388

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Moduli of Vector Bundles by Masaki Maruyama Pdf

"Contains papers presented at the 35th Taniguchi International Symposium held recently in Sanda and Kyoto, Japan. Details the latest developments concerning moduli spaces of vector bundles or instantons and their application. Covers a broad array of topics in both differential and algebraic geometry."

Author : Andrej N. Tjurin
Publisher : Universitätsverlag Göttingen
Page : 330 pages
File Size : 50,9 Mb
Release : 2008
Category : Vector bundles
ISBN : 9783938616741

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Vector Bundles by Andrej N. Tjurin Pdf

This is the first volume of a three volume collection of Andrey Nikolaevich Tyurin's Selected Works. It includes his most interesting articles in the field of classical algebraic geometry, written during his whole career from the 1960s. Most of these papers treat different problems of the theory of vector bundles on curves and higher dimensional algebraic varieties, a theory which is central to algebraic geometry and most of its applications.

Author : Shoshichi Kobayashi
Publisher : Princeton University Press
Page : 317 pages
File Size : 48,8 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400858682

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Differential Geometry of Complex Vector Bundles by Shoshichi Kobayashi Pdf

Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Francesco Scattone
Publisher : American Mathematical Soc.
Page : 86 pages
File Size : 44,5 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 : János Kollár
Publisher : Cambridge University Press
Page : 491 pages
File Size : 45,9 Mb
Release : 2023-04-30
Category : Mathematics
ISBN : 9781009346108

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Families of Varieties of General Type by János Kollár Pdf

The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.

Author : J. Le Potier
Publisher : Cambridge University Press
Page : 260 pages
File Size : 46,8 Mb
Release : 1997-01-28
Category : Mathematics
ISBN : 0521481821

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Lectures on Vector Bundles by J. Le Potier Pdf

This work consists of two sections on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The author also discusses the construction and elementary properties of the moduli spaces of stable bundles. In particular Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, and treats Mumford's geometric invariant theory. The second part centers on the structure of the moduli space of semistable sheaves on the projective plane. The author sketches existence conditions for sheaves of given rank, and Chern class and construction ideas in the general context of projective algebraic surfaces. Professor Le Potier provides a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.