  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.
