Bott's formula and enumerative geometry

Details Bott's formula and enumerative geometry Bott's formula and enumerative geometry

1994-11-10

arxiv.org/abs/alg-geom/9411005v1

Mathematics

Algebraic Geometry

22 pages, amslatex 1.1 The paper is a considerably expanded version of our previous eprint alg-geom/9409006 which had the titl

Scientific paper

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.

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