Prime arithmetic Teichmuller discs in H(2)

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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.
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

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Geometric Topology, 32G15 (37C35 37D50 30F30 14H55 30F35)

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http://salesiana.dossiersoluciones.com/handle/123456789/130528

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0401056
 http://arxiv.org/abs/math/0401056

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arXiv