Counting lattice points in compactified moduli spaces of curves

Abstract

We define and count lattice points in the moduli space M g;n of stable genus g curves with n labeled points. This extends a construction of the second author for the uncompactified moduli space M g;n. The enumeration produces polynomials whose top degree coefficients are tautological intersection numbers on M g;n and whose constant term is the orbifold Euler characteristic of M g;n.We prove a recursive formula which can be used to effectively calculate these polynomials. One consequence of these results is a simple recursion relation for the orbifold Euler characteristic of M g;n.