Prime arithmetic Teichmuller discs in H(2)

Details Prime arithmetic Teichmuller discs in H(2) Prime arithmetic Teichmuller discs in H(2)

2004-01-07

arxiv.org/abs/math/0401056v2

Mathematics

Geometric Topology

Accepted for publication in Israel Journal of Mathematics. A previous version circulated with the title "Square-tiled surfaces

Scientific paper

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.

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