Bott’s formula and enumerative geometry

Ellingsrud, Geir; Strømme, Stein

doi:10.1090/S0894-0347-96-00189-0

Bott’s formula and enumerative geometry
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by Geir Ellingsrud and Stein Arild Strømme PDF

J. Amer. Math. Soc. 9 (1996), 175-193 Request permission

Abstract:

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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