Bott's formula and enumerative geometry
Abstract
Description
We outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of Bott. As an example, Gromov-Witten numbers of twisted cubic and elliptic quartic curves on some general complete intersection in projective space are computed. The results are consistent with predictions made from mirror symmetry computations. We also compute degrees of some loci in the linear system of plane curves of degrees less than 10, like those corresponding to sums of powers of linear forms, and curves carrying inscribed polygons.
22 pages, amslatex 1.1 The paper is a considerably expanded version of our previous eprint alg-geom/9409006 which had the title "Counting twisted cubics on general complete intersections"
22 pages, amslatex 1.1 The paper is a considerably expanded version of our previous eprint alg-geom/9409006 which had the title "Counting twisted cubics on general complete intersections"