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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Intersections of $\mathbb{Q}$-divisors
on Kontsevich's moduli space $\overline M_{0,n}(\mathbb P^r,d)$
and enumerative geometry


Author: Rahul Pandharipande
Journal: Trans. Amer. Math. Soc. 351 (1999), 1481-1505
MSC (1991): Primary 14N10, 14H10; Secondary 14E99
MathSciNet review: 1407707
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Abstract: The theory of $\mathbb Q$-Cartier divisors on the space of $n$-pointed, genus 0, stable maps to projective space is considered. Generators and Picard numbers are computed. A recursive algorithm computing all top intersection products of $\mathbb Q$-divisors is established. As a corollary, an algorithm computing all characteristic numbers of rational curves in $\mathbb P^r$ is proven (including simple tangency conditions). Computations of these characteristic numbers are carried out in many examples. The degree of the 1-cuspidal rational locus in the linear system of degree $d$ plane curves is explicitly evaluated.


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Additional Information

Rahul Pandharipande
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Address at time of publication: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: rahulp@cco.caltech.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-01909-1
PII: S 0002-9947(99)01909-1
Received by editor(s): March 11, 1996
Additional Notes: Partially supported by an NSF Post-Doctoral Fellowship.
Article copyright: © Copyright 1999 American Mathematical Society