#### Filter Results:

- Full text PDF available (4)

#### Publication Year

2004

2011

- This year (0)
- Last 5 years (0)
- Last 10 years (3)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Gabriela Schmithüsen
- Experimental Mathematics
- 2004

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)

- Frank Herrlich, Gabriela Schmithüsen
- 2008

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)

— We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of GL+(2, R) avoiding the set of mappings of norm less than 1 appear as Veech groups of tame non-compact flat surfaces which are Loch Ness monsters. Conversely, a Veech group of any tame flat surface is either countable, or one of three specific… (More)

- ‹
- 1
- ›