Wall-crossing formulas, Bott residue formula and the Donaldson invariants of rational surfaces

Details Wall-crossing formulas, Bott residue formula and the Donaldson invariants of rational surfaces Wall-crossing formulas, Bott residue formula and the Donaldson invariants of rational surfaces

1995-06-23

arxiv.org/abs/alg-geom/9506019v2

Mathematics

Algebraic Geometry

We correct some missing attributions and citations. In particular this applies to the cited paper of Kotschick and Lisca "Inst

Scientific paper

We study the Donaldson invariants of rational surfaces and their dependence on the chambers in the ample cone. We build on a previous joint paper in which we have expressed the change of the Donaldson invariants on an algebraic surface $S$ under crossing a so-called good wall in terms of certain intersection numbers on Hilbert schemes of points on $S$. In the current paper we assume that $S$ is rational. Thish enables us to apply the Bott residue theorem to evaluate these intersection numbers with the help of a computer. Combining this with the blowup formulas we obtain an algorithm for computing the Donaldson invariants of all rational surfaces in almost all chambers. In particular we compute all the $SU(2)$- and $SO(3)$-Donaldson invariants of the projective plane of degree at most 50.

Affiliated with

Also associated with

No associations

Rating

Wall-crossing formulas, Bott residue formula and the Donaldson invariants of rational 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 Wall-crossing formulas, Bott residue formula and the Donaldson invariants of rational surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Wall-crossing formulas, Bott residue formula and the Donaldson invariants of rational surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-531344