Results 1 
3 of
3
NONVEECH SURFACES IN Hhyp(4) ARE GENERIC
, 2014
"... We show that every surface in the component Hhyp(4), that is the moduli space of pairs (M, ω) where M is a genus three hyperelliptic Riemann surface and ω is an Abelian differential having a single zero on M, is either a Veech surface or a generic surface, i.e. its GL+(2,R)orbit is either a close ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We show that every surface in the component Hhyp(4), that is the moduli space of pairs (M, ω) where M is a genus three hyperelliptic Riemann surface and ω is an Abelian differential having a single zero on M, is either a Veech surface or a generic surface, i.e. its GL+(2,R)orbit is either a closed or a dense subset ofHhyp(4). The proof develops new techniques applicable in general to the problem of classifying orbit closures, especially in low genus. Combined with work of Matheus and the second author, a corollary is that there are at most finitely many nonarithmetic Teichmüller curves (closed orbits of surfaces not covering the torus) inHhyp(4).
A codingfree simplicity criterion for the Lyapunov exponents of Teichmüller curves, preprint arXiv:1210.2157
, 2012
"... ABSTRACT. In this note we show that the results of H. Furstenberg on the Poisson boundary of lattices of semisimple Lie groups allow to deduce simplicity properties of the Lyapunov spectrum of the KontsevichZorich cocycle of Teichmüller curves in moduli spaces of Abelian differentials without the ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
ABSTRACT. In this note we show that the results of H. Furstenberg on the Poisson boundary of lattices of semisimple Lie groups allow to deduce simplicity properties of the Lyapunov spectrum of the KontsevichZorich cocycle of Teichmüller curves in moduli spaces of Abelian differentials without the usage of codings of the Teichmüller flow. As an application, we show the simplicity of some Lyapunov exponents in the setting of (some) Prym Teichmüller curves of genus 4 where a codingbased approach seems hard to implement because of the poor knowledge of the Veech group of these Teichmüller curves. Finally, we extend the discussion in this note to show the simplicity of Lyapunov exponents coming from (high weight) variations of Hodge structures associated to mirror quintic CalabiYau threefolds. CONTENTS