Moduli Spaces and Vector Bundles

by Edited by Leticia Brambila-Paz , Steven B. Bradlow , Oscar García-Prada , S. Ramanan

• ISBN13: 9780521734714
• ISBN10: 0521734711
• Edition: 1st
• Format: Paperback
• Copyright: 2009-07-06
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface	p. vii
Acknowledgments	p. ix
Lecture Notes	p. 1
Lectures on Principal Bundles	p. 2
Brill-Noether Theory for Stable Vector Bundles	p. 29
Introduction to Fourier-Mukai and Nahm Transforms with an Application to Coherent Systems on Elliptic Curves	p. 51
Geometric Invariant Theory	p. 99
Deformation Theory for Vector Bundles	p. 128
The Theory of Vector Bundles on Algebraic Curves with Some Applications	p. 165
Survey Articles	p. 211
Moduli of Sheaves from Moduli of Kronecker Modules	p. 212
Coherent Systems: a Brief Survey	p. 229
Higgs Bundles Surface and Group Representations	p. 265
Quotients by Non-Reductive Algebraic Group Actions	p. 311
Dualities on T*SUX (2,Ox)	p. 367
Moduli Spaces for Principal Bundles	p. 388
Research Articles	p. 425
Beilinson Type Spectral Sequences on Scrolls	p. 426
Coherent Systems on a Nodal Curve	p. 437
Brill-Noether Bundles and Coherent Systems on Special Curves	p. 456
Higgs Bundles in the Vector Representation	p. 473
Moduli Spaces of Torsion Free Sheaves on Nodal Curves and Generalisations - I	p. 484
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