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

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dc.creatorEllingsrud, Geir
dc.creatorGöttsche, Lothar
dc.date1995-06-23
dc.date1995-07-15
dc.date.accessioned2026-07-07T08:57:58Z
dc.date.available2026-07-07T08:57:58Z
dc.descriptionWe 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.
dc.descriptionWe correct some missing attributions and citations. In particular this applies to the cited paper of Kotschick and Lisca "Instanton invariants via topology", which contains some ideas which have been important for this work. AMSLaTeX
dc.identifierhttps://arxiv.org/abs/alg-geom/9506019
dc.identifierhttp://arxiv.org/abs/alg-geom/9506019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/147145
dc.subjectAlgebraic Geometry
dc.titleWall-crossing formulas, Bott residue formula and the Donaldson invariants of rational surfaces
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