Lecture Notes in Mathematics: Elliptic Surfaces with pg = 1: Smooth Classification

Niss, M.; Morgan, John W.; O'Grady, Kieran G.

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.

Details

Published by: Springer

Publication Date: 1993-08-30

Format: Paperback

ISBN-13: 9783540566748

DOI: 10.1007/BFb0086765

Dimensions: 235cm x155cm

Pages: 224