Institut de Mathématiques de Luminy

Abstract 2004-2

Hubert Pascal, Lelièvre Samuel.
Square-tiled surfaces in H(2).

This is a study of square-tiled translation surfaces in the stratum H(2) and their SL(2 , R)-orbits or Teichmüller discs, which are arithmetic. We prove that for prime n > 3 translation surfaces tiled by n squares fall into two Teichmüller discs, only one of them with elliptic points, and that the genus of these discs has a cubic growth rate in n.

Keywords: Teichmüller discs, square-tiled surfaces, Weierstrass points.
MSC: 32G15 (37C35 30F30 14H55 30F35)


Last update : january 23, 2004, EL.