Ebook: Differential Topology of Complex Surfaces: Elliptic Surfaces with p g =1: Smooth Classification

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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This book is about the smooth classification of a certain class of algebraicsurfaces, namely regular ellipticsurfaces of geometric genus one, i.e. elliptic surfaces withb1 = 0 and b2+ = 3. The authors give a completeclassification of these surfaces up to diffeomorphism. Theyachieve this result by partially computing one of Donalson'spolynomial invariants. The computation is carried out usingtechniques from algebraic geometry. 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. Somefamiliarity with the basic facts of the theory of moduliofsheaves and bundles on a surface is also assumed. This workgives a good and fairly comprehensive indication of how themethods of algebraic geometry can be used to computeDonaldson invariants.