2014/08/28 by Florian Nisbach, Nisbach, Florian
Engineering · Mathematics · #11G32 #14H30 #32G15 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.AG #math.GT #msc:11G32 #msc:14H30 #msc:32G15
paper · pdf · doi:10.48550/arxiv.1408.6769
43 pages
arxiv created 2014/08/28 · openalex publication_date 2014/08/28 · arxiv updated 2014/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a rather special class of translation surfaces (called M-Origamis in this work) that are obtained from dessins by a construction introduced by Martin Möller. We give a new proof with a more combinatorial flavour of Möller's theorem that Gal(ℚ/ℚ) acts faithfully on the Teichmüller curves of M-Origamis and extend his result by investigating the Galois action in greater detail. We determine the Strebel directions and corresponding cylinder decompositions of an M-Origami, as well as its Veech group, which contains the modular group Γ(2) and is closely connected to a certain group of symmetries of the underlying dessin. Finally, our calculations allow us to give explicit examples of Galois orbits of M-Origamis and their Teichmüller curves.