The canonical class and the $C^\infty$ properties of Kähler surfaces

Details The canonical class and the $C^\infty$ properties of Kähler surfaces The canonical class and the $C^\infty$ properties of Kähler surfaces

1995-03-10

arxiv.org/abs/alg-geom/9503004v2

Mathematics

Algebraic Geometry

38 pages. Hardcopy available upon request. Latex 2e with amsart v. 1.2 or AMSlaTeX version 1.1. reason for resubmission: Chang

Scientific paper

We give a self contained proof using Seiberg Witten invariants that for K\"ahler surfaces with non negative Kodaira dimension (including those with $p_g = 0$) the canonical class of the minimal model and the $(-1)$-curves, are oriented diffeomorphism invariants up to sign. This implies that the Kodaira dimension is determined by the underlying differentiable manifold (Van de Ven Conjecture). We use a set up that replaces generic metrics by the construction of a localised Euler class of an infinite dimensional bundle with a Fredholm section. This allows us to compute the Seiberg Witten invariants of all elliptic surfaces with excess intersection theory. 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.

Affiliated with

Also associated with

No associations

Rating

The canonical class and the $C^\infty$ properties of Kähler surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The canonical class and the $C^\infty$ properties of Kähler surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The canonical class and the $C^\infty$ properties of Kähler surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-63408