Intersections numbers on the compact variety of rational ruled surfaces
Abstract
Description
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 Plücker 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.
19 pages, change of title, the last conjecture has been removed, to appear in the Proceedings of the Quantum topology conference in Hanoi 2007
19 pages, change of title, the last conjecture has been removed, to appear in the Proceedings of the Quantum topology conference in Hanoi 2007