Grassmannians Moduli Spaces And Vector Bundles

Author : David Ellwood,David A. Ellwood,Emma Previato
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 54,9 Mb
Release : 2011
Category : Commutative rings
ISBN : 9780821852057

Get Book

Grassmannians, Moduli Spaces and Vector Bundles by David Ellwood,David A. 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 : Leticia Brambila-Paz,Steven B. Bradlow,Oscar García-Prada,S. Ramanan
Publisher : Cambridge University Press
Page : 506 pages
File Size : 44,8 Mb
Release : 2009-05-21
Category : Mathematics
ISBN : 9781139480048

Get Book

Moduli Spaces and Vector Bundles by Leticia Brambila-Paz,Steven B. Bradlow,Oscar García-Prada,S. Ramanan Pdf

Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory. Peter E. Newstead has been a leading figure in this field almost from its inception and has made many seminal contributions to our understanding of moduli spaces of stable bundles. This volume has been assembled in tribute to Professor Newstead and his contribution to algebraic geometry. Some of the subject's leading experts cover foundational material, while the survey and research papers focus on topics at the forefront of the field. This volume is suitable for both graduate students and more experienced researchers.

Author : Andrej N. Tjurin
Publisher : Universitätsverlag Göttingen
Page : 330 pages
File Size : 43,6 Mb
Release : 2008
Category : Vector bundles
ISBN : 9783938616741

Get Book

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 : Christian Okonek,Michael Schneider,Heinz Spindler
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 47,8 Mb
Release : 2011-07-07
Category : Mathematics
ISBN : 9783034801508

Get Book

Vector Bundles on Complex Projective Spaces by Christian Okonek,Michael Schneider,Heinz Spindler Pdf

These lecture notes are intended as an introduction to the methods of classi?cation of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = P . According to Serre (GAGA) the class- n cation of holomorphic vector bundles is equivalent to the classi?cation of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some fundamental results from these ?elds are summarized at the beginning. One of the authors gave a survey in the S ́eminaire Bourbaki 1978 on the current state of the classi?cation of holomorphic vector bundles over P . This lecture then served as the basis for a course of lectures n in G ̈ottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the - troductory nature of this book we have had to leave out some di?cult topics such as the restriction theorem of Barth. As compensation we have appended to each section a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of pa- graphs. Each section is preceded by a short description of its contents.

Author : Valery Alexeev
Publisher : American Mathematical Soc.
Page : 249 pages
File Size : 42,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821868997

Get Book

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 : Christian Okonek,Heinz Spindler,Michael Schneider
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 44,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475714609

Get Book

Vector Bundles on Complex Projective Spaces by Christian Okonek,Heinz Spindler,Michael Schneider Pdf

These lecture notes are intended as an introduction to the methods of classification of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = Fn. According to Serre (GAGA) the classification of holomorphic vector bundles is equivalent to the classification of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some funda mental results from these fields are summarized at the beginning. One of the authors gave a survey in the Seminaire Bourbaki 1978 on the current state of the classification of holomorphic vector bundles overFn. This lecture then served as the basis for a course of lectures in Gottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the introductory nature of this book we have had to leave out some difficult topics such as the restriction theorem of Barth. As compensation we have appended to each sec tion a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of paragraphs. Each section is preceeded by a short description of iv its contents.

Author : Richard Wentworth,Graeme Wilkin
Publisher : World Scientific
Page : 412 pages
File Size : 54,5 Mb
Release : 2018-06-28
Category : Mathematics
ISBN : 9789813229105

Get Book

The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles by Richard Wentworth,Graeme Wilkin Pdf

In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngô Bau Châu's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field.

Author : Steven Dale Cutkosky
Publisher : American Mathematical Soc.
Page : 260 pages
File Size : 54,6 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0821856588

Get Book

Vector Bundles and Representation Theory by Steven Dale Cutkosky Pdf

This volume contains 13 papers from the conference on ''Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory''. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S1$ fixed points in Quot-schemes and mirror principle computations for Grassmanians by S.-T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.

Author : Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa
Publisher : Cambridge University Press
Page : 451 pages
File Size : 53,5 Mb
Release : 2015-01-15
Category : Mathematics
ISBN : 9781107647558

Get Book

Recent Advances in Algebraic Geometry by Christopher D. Hacon,Mircea Mustaţă,Mihnea Popa Pdf

A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

Author : Shigeru Mukai
Publisher : Cambridge University Press
Page : 528 pages
File Size : 44,6 Mb
Release : 2003-09-08
Category : Mathematics
ISBN : 0521809061

Get Book

An Introduction to Invariants and Moduli by Shigeru Mukai Pdf

Sample Text

Author : Valery Alexeev
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 46,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821889541

Get Book

Compact Moduli Spaces and Vector Bundles by Valery Alexeev Pdf

Author : Shrawan Kumar
Publisher : Cambridge University Press
Page : 539 pages
File Size : 40,8 Mb
Release : 2021-11-25
Category : Mathematics
ISBN : 9781316518168

Get Book

Conformal Blocks, Generalized Theta Functions and the Verlinde Formula by Shrawan Kumar Pdf

This book gives a complete proof of the Verlinde formula and of its connection to generalized theta functions.

Author : Jan Arthur Christophersen,Kristian Ranestad
Publisher : Springer
Page : 326 pages
File Size : 48,7 Mb
Release : 2018-11-24
Category : Mathematics
ISBN : 9783319948812

Get Book

Geometry of Moduli by Jan Arthur Christophersen,Kristian Ranestad Pdf

The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in which moduli theory is advancing. These include the geometry of moduli spaces, non-reductive geometric invariant theory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies of curves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.

Author : Tommaso de Fernex,Brendan Hassett,Mircea Mustaţă,Martin Olsson,Mihnea Popa,Richard Thomas
Publisher : American Mathematical Soc.
Page : 655 pages
File Size : 40,7 Mb
Release : 2018-06-01
Category : Geometry, Algebraic
ISBN : 9781470435776

Get Book

Algebraic Geometry: Salt Lake City 2015 (Part 1) by Tommaso de Fernex,Brendan Hassett,Mircea Mustaţă,Martin Olsson,Mihnea Popa,Richard Thomas Pdf

This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 537 pages
File Size : 48,9 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9781108715775

Get Book

Integrable Systems and Algebraic Geometry by Ron Donagi,Tony Shaska Pdf

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.