Differential Topology of Complex Surfaces

Elliptic Surfaces with pg=1: Smooth Classification

  • Authors
  • John W. Morgan
  • Kieran G. O’Grady

Part of the Lecture Notes in Mathematics book series (LNM, volume 1545)

Table of contents

  1. Front Matter
    Pages I-VII
  2. John W. Morgan, Kieran G. O’Grady
    Pages 1-11
  3. John W. Morgan, Kieran G. O’Grady
    Pages 12-32
  4. John W. Morgan, Kieran G. O’Grady
    Pages 33-56
  5. John W. Morgan, Kieran G. O’Grady
    Pages 57-98
  6. John W. Morgan, Kieran G. O’Grady
    Pages 99-111
  7. John W. Morgan, Kieran G. O’Grady
    Pages 112-166
  8. John W. Morgan, Kieran G. O’Grady
    Pages 167-210
  9. Back Matter
    Pages 211-224

About this book

Introduction

This book is about the smooth classification of a certain class of algebraicsurfaces, namely regular elliptic surfaces of geometric genus one, i.e. elliptic surfaces with b1 = 0 and b2+ = 3. The authors give a complete classification of these surfaces up to diffeomorphism. They achieve this result by partially computing one of Donalson's polynomial invariants. The computation is carried out using techniques from algebraic geometry. In these computations both thebasic facts about the Donaldson invariants and the relationship of the moduli space of ASD connections with the moduli space of stable bundles are assumed known. Some familiarity with the basic facts of the theory of moduliof sheaves and bundles on a surface is also assumed. This work gives a good and fairly comprehensive indication of how the methods of algebraic geometry can be used to compute Donaldson invariants.

Keywords

Blowing up diffeomorphism differential topology elliptic surfaces four-manifolfds moduli space

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0086765
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-56674-8
  • Online ISBN 978-3-540-47628-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book