de Mathématiques de Luminy
Hubert Pascal, Lelièvre
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