Differential Topology of Complex Surfaces

Elliptic Surfaces with pg = 1: Smooth Classification
1993
ISBN: 978-3-540-56674-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1545, 224 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 365 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Morgan, John W.

O'Grady, Kieran G.

Weitere Mitwirkende

Niss, M.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.