Intersections of psi-classes on moduli spaces of m-stable curves

TL;DR

This paper develops recursive formulas to compute intersection numbers of psi-classes on moduli spaces of m-stable genus one curves, extending known results for stable curves.

Contribution

It introduces new recursion relations for intersection numbers on m-stable moduli spaces, generalizing the classical string and dilaton equations.

Findings

Recursion formulas for m-stable curves of genus one

Extension of classical intersection number computations

Explicit determination of intersection numbers using recursions

Abstract

We explain how to compute top-dimensional intersections of psi-classes on moduli spaces of m-stable curves. On the moduli spaces of Deligne-Mumford stable pointed curves of genus one, these intersection numbers are determined by two recursions, namely the string equation and the dilaton equation. We establish, for each integer m>0, an analogous pair of recursions which determine these intersection numbers on the moduli spaces of m-stable pointed curves of genus one.