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We study the Veech group of an origami, i.e. of a translation surface, tessellated by parallelograms. We show that it is isomorphic to the image of a certain subgroup of Aut + (F 2) in SL 2 (Z) ∼ = Out + (F 2). Based on this we present an algorithm that determines the Veech group. (Oriented) origamis (as defined in section 2.1) can be described as follows:(More)
In this article we give an introduction to origamis (often also called square-tiled surfaces) and their Veech groups. As main theorem we prove that in each genus there exist origamis, whose Veech groups are non congruence subgroups of SL 2 (Z). The basic idea of an origami is to obtain a topological surface from a few combina-torial data by gluing finitely(More)
In this chapter, we give an introduction to the theory of dessins d'enfants. They provide a charming concrete access to a special topic of arithmetic geometry: Curves defined over number fields can be described by such simple combina-torial objects as graphs embedded into topological surfaces. Dessins d'enfants are in some sense an answer of Grothendieck to(More)
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