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Algebraic Surfaces and Holomorphic Vector Bundles

  • Robert Friedman

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Robert Friedman
    Pages 1-5
  3. Robert Friedman
    Pages 7-24
  4. Robert Friedman
    Pages 25-58
  5. Robert Friedman
    Pages 59-83
  6. Robert Friedman
    Pages 85-112
  7. Robert Friedman
    Pages 113-139
  8. Robert Friedman
    Pages 141-165
  9. Robert Friedman
    Pages 167-195
  10. Robert Friedman
    Pages 197-243
  11. Robert Friedman
    Pages 245-276
  12. Back Matter
    Pages 315-328

About this book

Introduction

This book is based on courses given at Columbia University on vector bun­ dles (1988) and on the theory of algebraic surfaces (1992), as well as lectures in the Park City lIAS Mathematics Institute on 4-manifolds and Donald­ son invariants. The goal of these lectures was to acquaint researchers in 4-manifold topology with the classification of algebraic surfaces and with methods for describing moduli spaces of holomorphic bundles on algebraic surfaces with a view toward computing Donaldson invariants. Since that time, the focus of 4-manifold topology has shifted dramatically, at first be­ cause topological methods have largely superseded algebro-geometric meth­ ods in computing Donaldson invariants, and more importantly because of and Witten, which have greatly sim­ the new invariants defined by Seiberg plified the theory and led to proofs of the basic conjectures concerning the 4-manifold topology of algebraic surfaces. However, the study of algebraic surfaces and the moduli spaces of bundles on them remains a fundamen­ tal problem in algebraic geometry, and I hope that this book will make this subject more accessible. Moreover, the recent applications of Seiberg­ Witten theory to symplectic 4-manifolds suggest that there is room for yet another treatment of the classification of algebraic surfaces. In particular, despite the number of excellent books concerning algebraic surfaces, I hope that the half of this book devoted to them will serve as an introduction to the subject.

Keywords

Blowing up differential equation minimum moduli space vector bundle

Authors and affiliations

  • Robert Friedman
    • 1
  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1688-9
  • Copyright Information Springer-Verlag New York, Inc. 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7246-5
  • Online ISBN 978-1-4612-1688-9
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site