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arXiv · 1005.3120

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

Dawei Chen
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Abstract

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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Dawei Chen. 2010-05-18. Covers of the projective line and the moduli space of quadratic differentials. https://arxiv.org/abs/1005.3120

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