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Article Dans Une Revue Israel Journal of Mathematics Année : 2006

Prime arithmetic Teichmüller discs in H(2)

Résumé

It is well-known that Teichmüller 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 Teichmüller 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 Teichmüller 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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Dates et versions

hal-00001002 , version 1 (07-01-2004)
hal-00001002 , version 2 (27-10-2004)

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Pascal Hubert, Samuel Lelièvre. Prime arithmetic Teichmüller discs in H(2). Israel Journal of Mathematics, 2006, 151, pp.281-321. ⟨10.1007/BF02777365⟩. ⟨hal-00001002v2⟩
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