Moduli Spaces and Vector Bundles

by Leticia Brambila-Paz (Editor), Steven B. Bradlow (Editor), Oscar García-Prada (Editor), S. Ramanan (Editor)

Overview

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.

Product Details

ISBN-13:	9780521734714
Publisher:	Cambridge University Press
Publication date:	05/21/2009
Series:	London Mathematical Society Lecture Note Series , #359
Pages:	516
Product dimensions:	6.00(w) x 8.90(h) x 1.10(d)

About the Author

Leticia Brambila-Paz is a Professor Titular in the Centro de Investigacion en Matematicas at the University of Guanajuato, Mexico.

Steven B. Bradlow is a Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign.

Oscar García-Prada is a Research Professor in the Instituto de Ciencias Matematicas at Consejo Superior de Investigaciones Cientificas.

S. Ramanan is a Retired Distinguished Professor from the Tata Institute of Fundamental Research in Mumbai. He is currently an Adjunct Professor at the Chennai Mathematical Institute in India.

Table of Contents

Preface vii

Acknowledgments ix

Part I Lecture Notes 1

1 Lectures on Principal Bundles V. Balaji 2

2 Brill-Noether Theory for Stable Vector Bundles Ivona Grzegorczyk Montserrat Teixidor i Bigas 29

3 Introduction to Fourier-Mukai and Nahm Transforms with an Application to Coherent Systems on Elliptic Curves U. Bruzzo D. Hern?ndez Ruip?rez C. Tejero Prieto 51

4 Geometric Invariant Theory P. E. Newstead 99

5 Deformation Theory for Vector Bundles N. Nitsure 128

6 The Theory of Vector Bundles on Algebraic Curves with Some Applications S. Ramanan 165

Part II Survey Articles 211

7 Moduli of Sheaves from Moduli of Kronecker Modules L. ?lvarez-C?nsul A. King 212

8 Coherent Systems: a Brief Survey S. B. Bradlow 229

9 Higgs Bundles Surface and Group Representations Oscar Garc?a-Prada 265

10 Quotients by Non-Reductive Algebraic Group Actions Frances Kirwan 311

11 Dualities on T*SU_X (2,O_x) E. Previato 367

12 Moduli Spaces for Principal Bundles A.H.W. Schmitt 388

Part III Research Articles 425

13 Beilinson Type Spectral Sequences on Scrolls M. Aprodu V. Br?nzănescu 426

14 Coherent Systems on a Nodal Curve Usha N. Bhosle 437

15 Brill-Noether Bundles and Coherent Systems on Special Curves L. Brambila-Paz Angela Ortega 456

16 Higgs Bundles in the Vector Representation N. Hitchin 473

17 Moduli Spaces of Torsion Free Sheaves on Nodal Curves and Generalisations - I C.S. Seshadri 484