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Wall-Crossing Formulas, the Bott Residue Formula and the Donaldson Invariants of Rational Surfaces
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ellingsrud, Geir Gottsche, Lothar |
| Copyright Year | 1995 |
| Abstract | 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. |
| Starting Page | 307 |
| Ending Page | 329 |
| Page Count | 23 |
| File Format | PDF HTM / HTML |
| DOI | 10.1093/qmathj/49.3.307 |
| Volume Number | 49 |
| Alternate Webpage(s) | http://arxiv.org/pdf/alg-geom/9506019v2.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/alg-geom/9506019v2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1093/qmathj%2F49.3.307 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
