Journal of the American Mathematical Society

Author(s): Geir Ellingsrud; Stein Arild Strømme
Journal: J. Amer. Math. Soc. 9 (1996), 175-193.
MSC (1991): Primary 14N10, 14C17, 14Q99; Secondary 14C05, 14L30, 14M10
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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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Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 14N10, 14C17, 14Q99, 14C05, 14L30, 14M10

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

DOI: 10.1090/S0894-0347-96-00189-0
PII: S 0894-0347(96)00189-0
Keywords: Bott's residue formula, Gromov-Witten number, complete intersection, twisted cubic, torus action, ternary power sum, Darboux curve
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 of article: Copyright 1996, American Mathematical Society

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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