Differential Topology of Complex Surfaces : Elliptic Surfaces with pg=1: Smooth Classification / John W. Morgan, Kieran G. O’Grady

Date :

Type : Livre / Book

Langue / Language : anglais / English

ISBN : 978-3-540-47628-3

Géométrie différentielle

Géométrie algébrique

Topologie différentielle

Surfaces algébriques

Surfaces elliptiques

Classification Dewey : 510

Classification Dewey : 516.352

Niss, Millie (Collaborateur / collaborator)

Collection : Lecture notes in mathematics / Heidelberg : Springer , 2001-

Relation : Differential topology of complex surfaces : elliptic surfaces with pg=1 : smooth classification / John W. Morgan, Kieran G. O'Grady ; with the collaboration of Millie Niss / Berlin : Springer , cop. 1993

Résumé / Abstract : 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.