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 $\mathrm{Vol}{\mathcal{Q}}_{g,n}$ associated with the principal strata of the moduli spaces of quadratic differentials, and propose refinements of the conjectural formulas given in [12,4] for the large genus asymptotics of $\mathrm{Vol}{\mathcal{Q}}_{g,n}$ and of the associated area Siegel--Veech constants.

17 pages