Covers of the projective line and the moduli space of quadratic differentials

Details Covers of the projective line and the moduli space of quadratic differentials Covers of the projective line and the moduli space of quadratic differentials

2010-05-18

arxiv.org/abs/1005.3120v1

Mathematics

Algebraic Geometry

Scientific paper

Consider the 1-dimensional Hurwitz space parameterizing covers of P^1 branched at four points. We study its intersection with divisor classes on the moduli space of curves. As an application, we calculate the slope of the Teichmuller curve parameterizing square-tiled cyclic covers and recover the sum of its Lyapunov exponents obtained by Forni, Matheus and Zorich. Motivated by the work of Eskin, Kontsevich and Zorich, we exhibit a relation among the slope of Hurwitz spaces, the sum of Lyapunov exponents and the Siegel-Veech constant for the moduli space of quadratic differentials.

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