Recursion for Masur-Veech volumes of moduli spaces of quadratic differentials

TL;DR

This paper introduces a quadratic recursion relation for certain Hodge integrals, enabling efficient computation of Masur-Veech volumes of moduli spaces of quadratic differentials, which are important in Teichmüller dynamics.

Contribution

The authors derive a new quadratic recursion for linear Hodge integrals that simplifies the calculation of Masur-Veech volumes of moduli spaces of quadratic differentials.

Findings

Derived a quadratic recursion relation for Hodge integrals.

Provided an efficient computational method for Masur-Veech volumes.

Enhanced understanding of the structure of moduli spaces of quadratic differentials.

Abstract

We derive a quadratic recursion relation for the linear Hodge integrals of the form $\langle\tau_2^n\lambda_k\rangle$. These numbers are used in a formula for Masur-Veech volumes of moduli spaces of quadratic differentials discovered by Chen, M\"oller, and Sauvaget. Therefore, our recursion provides an efficient way of computing these volumes.