Volumes of strata of Abelian differentials and Siegel-Veech constants in large genera

Abstract

We state conjectures on the asymptotic behavior of the volumes of moduli spaces of Abelian differentials and their Siegel-Veech constants as genus tends to infinity. We provide certain numerical evidence, describe recent advances and the state of the art towards proving these conjectures.

Some background material is added on request of the referee. To appear in Arnold Math. Journal

Cited by in corpus (4)

• Masur-Veech volumes and intersection theory on moduli spaces of abelian differentials
• 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
• Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials