Convergence of integrals on the moduli spaces of curves and cographical matroids

TL;DR

This paper characterizes the convergence regions of specific local integrals on moduli spaces of curves by analyzing the combinatorial structure of associated graphs, providing insights into the interplay between geometry and combinatorics.

Contribution

It introduces a combinatorial criterion for the convergence of integrals on moduli spaces of curves based on graph structures, advancing understanding in algebraic geometry.

Findings

Convergence regions are explicitly described using graph combinatorics.

The results connect geometric properties of moduli spaces with graph theory.

Provides a framework for analyzing integrals in algebraic geometry contexts.

Abstract

We determine the convergence regions of certain local integrals on the moduli spaces of curves in neighborhoods of fixed stable curves in terms of the combinatorics of the corresponding graphs.