Counting lattice points in compactified moduli spaces of curves

Understand

We define and count lattice points in the moduli space of stable genus g curves with n labeled points.

• This extends a construction of the second author for the uncompactified moduli space.
• The enumeration produces polynomials with top degree coefficients tautological intersection numbers on the compactified moduli space and constant term the orbifold Euler characteristic of the compactified moduli space.
• We also prove a recursive formula which can be used to effectively calculate these polynomials.