Covers of the projective line and the moduli space of quadratic differentials
Algebraic Geometry
2010-05-19 v1 Dynamical Systems
Geometric Topology
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.
Keywords
Cite
@article{arxiv.1005.3120,
title = {Covers of the projective line and the moduli space of quadratic differentials},
author = {Dawei Chen},
journal= {arXiv preprint arXiv:1005.3120},
year = {2010}
}