Intersections numbers on the compact variety of rational ruled surfaces
Abstract
We consider the Quot scheme, Rd, 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 Rd 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 Rd. These numbers can be obtained directly from Vafa-Intriligator formula.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.