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Examples for Veech groups of origamis

Gabriela Schmithüsen

Proceedings of the III Iberoamerican Congress on Geometry. In: The Geometry of Riemann Surfaces and Abelian Varieties. Contemp. Math. 397, 2006 (p. 193 – 206).

We study infinite sequences of special translation surfaces, more precisely of origamis. We determine their Veech groups as certain well known congruence subgroups of SL(2,Z).
Our construction also yields in each moduli space M_g (g > 1) a Teichmüller curve whose normalisation is the projective line with three points removed. We obtain the same result for the
projective line with two points removed.