BOTTS FORMULA AND ENUMERATIVE GEOMETRY

We outline a strategy for computing intersection numbers on smooth var ieties with torus actions using a residue formula of Bott. As an examp le, Gromov-Witten numbers of twisted cubic and elliptic quartic curves on some general complete intersection in projective space are compute d. The results are consistent with predictions made from mirror symmet ry computations. We also compute degrees of some loci in the linear sy stem of plane curves of degrees less than 10, like those corresponding to sums of powers of linear forms, and curves carrying inscribed poly gons.