Covers of the Projective Line and the Moduli Space of Quadratic Differentials
نویسنده
چکیده
Consider the Hurwitz space parameterizing covers of P branched at four points. We study its intersection with divisor classes on the moduli space of curves. As applications, we calculate the slope of Teichmüller curves parameterizing square-tiled cyclic covers. In addition, we come up with a relation among the slope of Teichmüller curves, the sum of Lyapunov exponents and the Siegel-Veech constant for the moduli space of quadratic differentials, which yields information for the effective cone of the moduli space of curves.
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