Bott’s formula and enumerative geometry

Ellingsrud, Geir; Strømme, Stein

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

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ISSN 1088-6834(online) ISSN 0894-0347(print)

Bott's formula and enumerative geometry

Authors: Geir Ellingsrud and Stein Arild Strømme
Journal: J. Amer. Math. Soc. 9 (1996), 175-193
MSC (1991): Primary 14N10, 14C17, 14Q99; Secondary 14C05, 14L30, 14M10
MathSciNet review: 1317230
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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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