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Differential topology of complex surfaces : elliptic surfaces with pg̳=1: smooth classification / John W. Morgan, Kieran G. O'Grady ; with the collaboration of Millie Niss.

By: Contributor(s): Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1545.Publication details: Berlin ; New York : Springer-Verlag, ©1993.Description: 1 online resource (224 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540476283
  • 3540476288
Subject(s): Additional physical formats: Print version:: Differential topology of complex surfaces.DDC classification:
  • 510 s 516.3/52 20
LOC classification:
  • QA3 .L28 no. 1545 QA573
Other classification:
  • 31.51
  • 31.52
  • 31.65
  • *14J27
  • 14-02
  • 57-02
  • 57R50
  • SI 850
  • 27
  • MAT 322f
  • MAT 576f
Online resources:
Contents:
Unstable polynomials of algebraic surfaces -- Identification of?3,r (S, H) with?3(S) -- Certain moduli spaces for bundles on elliptic surfaces with p g = 1 -- Representatives for classes in the image of the?-map -- The blow-up formula -- The proof of Theorem 1.1.1.
Action note:
  • digitized 2010 HathiTrust Digital Library committed to preserve
Summary: 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.
Holdings
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Includes bibliographical references (pages 219-221) and index.

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.

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Print version record.

Unstable polynomials of algebraic surfaces -- Identification of?3,r (S, H) with?3(S) -- Certain moduli spaces for bundles on elliptic surfaces with p g = 1 -- Representatives for classes in the image of the?-map -- The blow-up formula -- The proof of Theorem 1.1.1.

English.

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