# Prime arithmetic Teichmüller discs in $$\mathcal{H}(2)$$

@article{Hubert2004PrimeAT, title={Prime arithmetic Teichm{\"u}ller discs in \$\$\mathcal\{H\}(2)\$\$}, author={Pascal Hubert and Samuel Leli{\`e}vre}, journal={Israel Journal of Mathematics}, year={2004}, volume={151}, pages={281-321} }

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 $$\mathcal{H}(2)$$ 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… CONTINUE READING

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