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.
The Large genus asymptotic expansion of Masur-Veech volumes
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abstract
We study the asymptotic behavior of Masur-Veech volumes as the genus goes to infinity. We show the existence of a complete asymptotic expansion of these volumes that depends only on the genus and the number of singularities. The computation of the first term of this asymptotics expansion was a long standing problem. This problem was recently solved in by Aggarwal using purely combinatorial arguments, and then by D. Chen, M. Moeller, D. Zagier and the author using algebro-geometric insights. Our proof relies on a combination of both methods.
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math.GT 1years
2019 1verdicts
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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.