%0 Generic %1 Chen2010 %A Chen, Dawei %D 2010 %K covers moduli projective %T Covers of the projective line and the moduli space of quadratic differentials %U http://arxiv.org/abs/1005.3120 %X 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.

@misc{Chen2010, 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. }, added-at = {2010-05-20T11:11:01.000+0200}, author = {Chen, Dawei}, biburl = {https://www.bibsonomy.org/bibtex/2bb2115ffdcb6ed4abf136f2aa2622a83/uludag}, description = {[1005.3120] Covers of the projective line and the moduli space of quadratic differentials}, interhash = {27ca738edd713f0e168cb99b5229334b}, intrahash = {bb2115ffdcb6ed4abf136f2aa2622a83}, keywords = {covers moduli projective}, note = {cite arxiv:1005.3120 }, timestamp = {2010-05-20T11:11:01.000+0200}, title = {Covers of the projective line and the moduli space of quadratic differentials}, url = {http://arxiv.org/abs/1005.3120}, year = 2010 }