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

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- by Rahul Pandharipande PDF
- Trans. Amer. Math. Soc.
**351**(1999), 1481-1505 Request permission

## 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.## References

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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
- MR Author ID: 357813
- Email: rahulp@cco.caltech.edu
- Received by editor(s): March 11, 1996
- Additional Notes: Partially supported by an NSF Post-Doctoral Fellowship.
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**351**(1999), 1481-1505 - MSC (1991): Primary 14N10, 14H10; Secondary 14E99
- DOI: https://doi.org/10.1090/S0002-9947-99-01909-1
- MathSciNet review: 1407707