 

Rogier Brussee
The Canonical Class and the C^{∞} Properties of Kähler Surfaces


Published: 
December 31, 1996 
Keywords: 
Surfaces, 4manifolds, Seiberg Wittentheory, ∞dimensional intersection theory 
Subject: 
Primary: 14J, 57N13. Secondary: 58B, 57R20 


Abstract
We give a self contained proof that
for Kähler surfaces with nonnegative Kodaira dimension,
the canonical class of the minimal model and the
(1)curves are oriented diffeomorphism invariants up to sign.
This includes the case p_{g} = 0.
It implies that the Kodaira dimension is determined by the underlying
differentiable manifold.
We then reprove that the multiplicities of the elliptic
fibration are determined by the underlying oriented manifold, and that
the plurigenera of a surface are oriented diffeomorphism invariants.
We also compute the Seiberg Witten invariants of all Kähler
surfaces of nonnegative Kodaira dimension.
The proof uses a set up of Seiberg Witten theory that replaces generic
metrics by the construction of a localised Euler class of an infinite
dimensional bundle with a Fredholm section. This makes the
techniques of excess intersection available in gauge theory


Author information
Fakultät für Mathematik Universität Bielefeld, Postfach 100131, 33501 Bielefeld
brussee@mathematik.unibielefeld.de

