Masur–Veech volumes of quadratic differentials and their asymptotics

Abstract

Based on the Chen–Möller–Sauvaget formula, we apply the theory of integrable systems to derive three equations for the generating series of the Masur–Veech volumes VolQg,n associated with the principal strata of the moduli spaces of quadratic differentials, and propose refinements of the conjectural formulas given in Delecroix et al. [11] and Aggarwal et al. [4] for the large genus asymptotics of VolQg,n and of the associated area Siegel–Veech constants.