de Mathématiques de Luminy
Hubert Pascal, Lelièvre Samuel.
Square-tiled surfaces in (2).
This is a study of square-tiled translation surfaces in the stratum (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.
MSC: 32G15 (37C35 30F30 14H55 30F35)