Differential Topology of Complex Surfaces: Elliptic Surfaces with Pg = 1: Smooth Classification

Elliptic Surfaces with pg = 1: Smooth Classification

Author: John W. Morgan and Kieran G. O'Grady Series: Lecture Notes in Mathematics

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This book is about the smooth classification of a certainclass of algebraicsurfaces, namely regular ellipticsurfaces of geometric genus one, i.e. In these computationsboth thebasic facts about the Donaldson invariants and therelationship of the moduli space of ASD connections with themoduli space of stable bundles are assumed known.

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This monograph concerns the smooth classification of a certain class of algebraic surfaces, namely regular elliptic surfaces of geometric genus one, (elliptic surfaces with bl = 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 Donaldson's polynomial invariants. The computation is carried out using techniques from algebraic geometry. In these computations, both the basic 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 moduli of sheaves and bundles on a surface is also assumed.