Year: 2007
Type: preprint
Abstract: As main result we show that for each g > 1 there is some translation surface of genus g whose Veech group is a non congruence subgroup of SL(2,Z). We use origamis/square-tiled surfaces to produce our examples. The article is divided into two parts: In the first part we introduce translation surfaces, origamis, Veech groups and Teichmueller curves and show for two origamis in genus 2 that their Veech groups are non congruence groups; in the second part we provide a technique that produces sequences of origamis whose Veech groups are decreasing. This is used to prove the main result.
Source: arXiv (Cornell University)
Author: Schmithuesen, Gabriela
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1659290272