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 Vol 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 Vol Q g,n and of the associated area Siegel-Veech constants.

Recursion for Masur-Veech Volumes of Moduli Spaces of Quadratic Differentials

“…Another integrable hierarchy of partial differential equations for Hodge integrals, namely, the intermediate long-wave hierarchy, is discovered in [4]. Based on the equations of that hierarchy, a number of other efficient recursions for Masur-Veech volumes are derived in [12]. The recursions of [12] have an advantage in that they are formulated in terms of the volumes themselves rather than single Hodge integrals.…”

“…Based on the equations of that hierarchy, a number of other efficient recursions for Masur-Veech volumes are derived in [12]. The recursions of [12] have an advantage in that they are formulated in terms of the volumes themselves rather than single Hodge integrals.…”