Skip to Main content Skip to Navigation
Theses

Surfaces de Veech arithmétiques en genre deux: disques de Teichmüller, groupes de Veech et constantes de Siegel-Veech

Abstract : On the moduli spaces of abelian differentials exists a natural action of SL(2,R). Its orbits, called Teichmüller discs, project in the moduli spaces of Riemann surfaces to complex geodesics. Pulling back the form dz of the standard torus by coverings branched over a single point, one obtains the square-tiled surfaces, integer points of the moduli spaces of abelian differentials. We study in detail the Teichmüller discs of integer points of the moduli space of abelian differentials in genus two with a double zero: number of Teichmüller discs for each number of square tiles, and their geometry; algebraic properties of the stabilisers (subgroups of SL(2,Z) which are not congruence subgroups); asymptotic behaviour of the Siegel-Veech constants (coefficients of the quadratic growth rates of closed geodesics) when the number of tiles tends to infinity.
Document type :
Theses
Complete list of metadata

Cited literature [80 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00008722
Contributor : Samuel Lelièvre <>
Submitted on : Tuesday, March 8, 2005 - 12:27:01 PM
Last modification on : Thursday, January 7, 2021 - 4:12:40 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:00:33 PM

Identifiers

  • HAL Id : tel-00008722, version 1

Citation

Samuel Lelièvre. Surfaces de Veech arithmétiques en genre deux: disques de Teichmüller, groupes de Veech et constantes de Siegel-Veech. Mathématiques [math]. Université Rennes 1, 2004. Français. ⟨tel-00008722⟩

Share

Metrics

Record views

420

Files downloads

451