Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials

Abstract

We describe a conjectural formula via intersection numbers for the Masur-Veech volumes of strata of quadratic differentials with prescribed zero orders, and we prove the formula for the case when the zero orders are odd. For the principal strata of quadratic differentials with simple zeros, the formula reduces to compute the top Segre class of the quadratic Hodge bundle, which can be further simplified to certain linear Hodge integrals. An appendix proves that the intersection of this class with $\psi$-classes can be computed by Eynard-Orantin topological recursion. As applications, we analyze numerical properties of Masur-Veech volumes, area Siegel-Veech constants and sums of Lyapunov exponents of the principal strata for fixed genus and varying number of zeros, which settles the corresponding conjectures due to Grivaux-Hubert, Fougeron, and elaborated in [the7]. We also describe conjectural formulas for area Siegel-Veech constants and sums of Lyapunov exponents for arbitrary affine invariant submanifolds, and verify them for the principal strata.

References in corpus (4)

• admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves
• Large Genus Asymptotics for Intersection Numbers and Principal Strata Volumes of Quadratic Differentials
• Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves
• The area is a good enough metric

Cited by in corpus (7)

• admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves
• Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves
• Variation of Hodge structure and enumerating tilings of surfaces by triangles and squares
• An intersection-theoretic proof of the Harer-Zagier formula
• Some Generalizations of Mirzakhani's Recursion and Masur-Veech Volumes via Topological Recursions
• Stable tree expressions with Omega-classes and Double Ramification cycles
• Higher genus meanders and Masur-Veech volumes