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

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

2000-06-22

arxiv.org/abs/math/0006171v1

Mathematics

Algebraic Geometry

Scientific paper

10.1007/s002220100142

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.

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