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Differential Topology of Complex Surfaces

Elliptic Surfaces with pg = 1: Smooth Classification

  • Book
  • © 1993

Overview

Authors:
  1. John W. Morgan
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  2. Kieran G. O’Grady
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1545)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VII
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  2. Introduction

    • John W. Morgan, Kieran G. O’Grady
    Pages 1-11

  3. Unstable polynomials of algebraic surfaces

    • John W. Morgan, Kieran G. O’Grady
    Pages 12-32

  4. Identification of δ3,r (S, H) with γ3(S)

    • John W. Morgan, Kieran G. O’Grady
    Pages 33-56

  5. Certain moduli spaces for bundles on elliptic surfaces with p g = 1

    • John W. Morgan, Kieran G. O’Grady
    Pages 57-98

  6. Representatives for classes in the image of the ν-map

    • John W. Morgan, Kieran G. O’Grady
    Pages 99-111

  7. The blow-up formula

    • John W. Morgan, Kieran G. O’Grady
    Pages 112-166

  8. The proof of Theorem 1.1.1

    • John W. Morgan, Kieran G. O’Grady
    Pages 167-210

  9. Back Matter

    Pages 211-224
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Differential Topology of Complex Surfaces

  • Book Subtitle: Elliptic Surfaces with pg = 1: Smooth Classification

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

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0086765

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-540-56674-8Published: 30 August 1993

  • eBook ISBN: 978-3-540-47628-3Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VII, 224

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Algebraic Geometry, Differential Geometry

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