Intersection numbers on the moduli spaces of stable maps in genus 0

Let V be a smooth, projective, convex variety. We define tautological psi and kappa classes on the moduli space of stable maps (M) over bar (0,n) (V), give a (graphical) presentation for these classes in terms of boundary strata, derive differential equations for the generating functions of the Gromov-Witten invariants of V twisted by these tautological classes, and prove that these intersection numbers are completely determined by the Gromov-Witten invariants of V. This results in families of genus zero cohomological field theory structures on the cohomology ring of V which includes the quantum cohomology as a special case.