Intersections numbers on the compact variety of rational ruled surfaces

Details Intersections numbers on the compact variety of rational ruled surfaces Intersections numbers on the compact variety of rational ruled surfaces

2006-04-24

arxiv.org/abs/math/0604503v2

Acta Mathematica Vietnamica, Vol 33/ 3, 2008, pp 529-546

Mathematics

Algebraic Geometry

19 pages, change of title, the last conjecture has been removed, to appear in the Proceedings of the Quantum topology conferen

Scientific paper

We consider the Quot scheme, R_{d}, compactifying the space of degree d maps from the projective line to the Grassmannian of lines. We give an algorithm for computing the degree of R_{d} under a "generalized Pl\"ucker embedding", this is a certain Gromov-Witten invariant. The approach is to apply the Atiyah-Bott localization formula for the natural C^{*}-action on R_{d}. These numbers can be obtained directly from Vafa-Intriligator formula.

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