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.
Description
[1005.3120] Covers of the projective line and the moduli space of quadratic differentials
%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
}