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Differential Topology of Complex Surfaces: Elliptic Surfaces with pg = 1: Smooth Classification: Lecture Notes in Mathematics, cartea 1545

M. Niss Autor John W. Morgan, Kieran G. O'Grady
en Limba Engleză Paperback – 30 aug 1993
This book is about the smooth classification of a certainclass 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.
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Specificații

ISBN-13: 9783540566748
ISBN-10: 3540566740
Pagini: 236
Ilustrații: VII, 224 p.
Dimensiuni: 155 x 235 x 12 mm
Greutate: 0.34 kg
Ediția:1993
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

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Research

Cuprins

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.