Prime arithmetic Teichmuller discs in H(2)

Pascal Hubert; Samuel Lelièvre

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Prime arithmetic Teichmuller discs in H(2)

Pascal Hubert·Samuel Lelièvre

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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.

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BibTeX RIS

Pascal Hubert, Samuel Lelièvre. 2004-10-28. Prime arithmetic Teichmuller discs in H(2). https://arxiv.org/abs/math/0401056

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