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Journal of the American Mathematical Society

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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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Additional Information
  • Geir Ellingsrud
  • Affiliation: Mathematical Institute University of Oslo P. O. Box 1053 N–0316 Oslo, Norway
  • Email: ellingsr@math.uio.no
  • Stein Arild Strømme
  • Affiliation: Mathematical Institute University of Bergen Allég 55 N–5007 Bergen, Norway
  • Email: stromme@mi.uib.no
  • Received by editor(s): August 22, 1994
  • Received by editor(s) in revised form: November 13, 1994

  • Dedicated: Dedicated to the memory of Alf Bjørn Aure, 1955–1994
  • © Copyright 1996 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 9 (1996), 175-193
  • MSC (1991): Primary 14N10, 14C17, 14Q99; Secondary 14C05, 14L30, 14M10
  • DOI: https://doi.org/10.1090/S0894-0347-96-00189-0
  • MathSciNet review: 1317230