Masur-Veech volumes of Qg,n are expressed as explicit polynomials in psi-class intersection numbers, and flat square-tiled counts are shown to match hyperbolic multicurve frequencies up to a normalization constant.
Masur-Veech volumes and intersection theory on moduli spaces of abelian differentials
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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.
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Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves
Masur-Veech volumes of Qg,n are expressed as explicit polynomials in psi-class intersection numbers, and flat square-tiled counts are shown to match hyperbolic multicurve frequencies up to a normalization constant.