Generating Functions in Algebraic Geometry and Sums over Trees

Abstract

We calculate generating functions for the Poincare polynomials of moduli spaces of pointed curves of genus zero and of Configuration Spaces of Fulton and MacPherson. We also prove that contributions of multiple coverings of curves in a Calabi-Yau threefold calculated via Kontsevich's compactification coincide with the prediction of Candelas et al., and Aspinwall and Morrison.