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

2010/05/18 by Dawei Chen, Chen, Dawei
Mathematics · #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.DS #math.GT

paper · pdf · doi:10.48550/arxiv.1005.3120

arxiv created 2010/05/18 · arxiv updated 2010/05/19

Abstract

Consider the 1-dimensional Hurwitz space parameterizing covers of P¹ 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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