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Differential Topology of Complex Surfaces : Elliptic Surfaces with Pg = 1: Smooth Classification - M. Niss

Differential Topology of Complex Surfaces

Elliptic Surfaces with Pg = 1: Smooth Classification

Paperback Published: 30th August 1993
ISBN: 9783540566748
Number Of Pages: 224

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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. 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.

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.

ISBN: 9783540566748
ISBN-10: 3540566740
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 224
Published: 30th August 1993
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.27
Weight (kg): 0.34