Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials

Abstract

We compute the asymptotics of the number of connected branched coverings of a torus as their degree goes to infinity and the ramification type stays fixed. These numbers are equal to the volumes of the moduli spaces of pairs (curve, holomorphic differential) with fixed multiplicities of zeros of the differential and have several applications in ergodic theory.

Cited by in corpus (82)

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• Semiclassical Entropy of BPS States in 4d $\mathcal{N}=2$ Theories and Counts of Geodesics
• Convergence of Siegel-Veech constants
• Mirror Symmetry for Plane Cubics Revisited
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• Asymptotic probability for connectedness
• Statistics of Square-tiled Surfaces: Symmetry and Short Loops
• Symmetric tensor representations,quasimodular forms, and weak Jacobi forms
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• A question on generalization of partition functions of CY 3-folds in String Theory
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• On the topology of H(2)
• Triangulations and volume form on moduli spaces of flat surfaces
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