Intersections of Q-Divisors on Kontsevich's Moduli Space ${\bar{M}}_{0,n}(P^r,d)$ and Enumerative Geometry

Abstract

The theory of 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 Q-Divisors is established. As a corollary, an algorithm computing all characteristic numbers of rational curves in 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.

arXiv commentAMSLaTex 31 pages

References in corpus (1)

• Quantum intersection rings

Cited by in corpus (1)

• A presentation for the Chow ring A^*(\bar{M}_{0,2}(P^1,2))