Prime arithmetic Teichmuller discs in H(2)
Geometric Topology
2007-06-13 v2
Abstract
It is well-known that Teichmuller discs that pass through "integer points'' of the moduli space of abelian differentials are very special: they are closed complex geodesics. However, the structure of these special Teichmuller discs is mostly unexplored: their number, genus, area, cusps, etc. We prove that in genus two all translation surfaces in H(2) tiled by a prime number n > 3 of squares fall into exactly two Teichmuller discs, only one of them with elliptic points, and that the genus of these discs has a cubic growth rate in n.
Keywords
Cite
@article{arxiv.math/0401056,
title = {Prime arithmetic Teichmuller discs in H(2)},
author = {Pascal Hubert and Samuel Lelièvre},
journal= {arXiv preprint arXiv:math/0401056},
year = {2007}
}
Comments
Accepted for publication in Israel Journal of Mathematics. A previous version circulated with the title "Square-tiled surfaces in H(2)''. Changes from v1: improved redaction, fixed typos, added references