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


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time, the focus of 4-manifold topology has shifted dramatically, at first be­ cause topological methods have largely superseded algebro-geometric meth­ ods in computing Donaldson invariants, and more importantly because of and Witten, which have greatly sim­ the new invariants defined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.


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
  • 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