Masur-Veech volumes and intersection theory on moduli spaces of abelian differentials

Abstract

We show that the Masur-Veech volumes and area Siegel-Veech constants can be obtained by intersection numbers on the strata of Abelian differentials with prescribed orders of zeros. As applications, we evaluate their large genus limits and compute the saddle connection Siegel-Veech constants for all strata. We also show that the same results hold for the spin and hyper-elliptic components of the strata.

arXiv comment67 pages, 3 figures

References in corpus (13)

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Cited by in corpus (20)

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• Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
• Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials
• Volumes of moduli spaces of flat surfaces
• A symmetric Bloch-Okounkov theorem
• Uniform Lower Bound for Intersection Numbers of $\psi$-Classes
• Masur-Veech volume of the gothic locus
• From Hurwitz numbers to Feynman diagrams: counting rooted trees in log gravity
• Masur--Veech volumes of quadratic differentials and their asymptotics
• Hyperelliptic Gorenstein curves and logarithmic differentials
• Regularized Integrals on Riemann Surfaces and Modular Forms
• Dynamical invariants and intersection theory on the flex and gothic loci
• Semiclassical Entropy of BPS States in 4d $\mathcal{N}=2$ Theories and Counts of Geodesics
• The factorial growth of topological recursion
• Quantum KdV hierarchy and shifted symmetric functions
• Higher genus meanders and Masur-Veech volumes
• Contribution of $n$-cylinder square-tiled surfaces to Masur-Veech volume of $\mathcal{H}(2g-2)$
• Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials