  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.
