Fundamental domains and generators for lattice Veech groups
Summary: The moduli space \( \mathcal{QM}_g\) of non-zero genus \(g\) quadratic differentials has a natural action of \[ G=\mathrm{GL}_2^+(\mathbb{R})\bigg/\left\langle\pm\begin{pmatrix} 1&0\\0&1\end{pmatrix}\right\rangle. \] The Veech group PSL\((X,q)\) is the stabilizer of \((X,q) \in \mathcal{QM}_g\) in \(G\). We describe a new algorithm for finding elements of \(\mathrm{PSL}(X,q)\) which, for lattice Veech groups, can be used to compute a fundamental domain and generators. Using our algorithm, we give the first explicit examples of generators and fundamental domains for non-arithmetic Veech groups where the genus of \(\mathbb H\big/\mathrm{PSL}(X,q)\) is greater than zero.
scientific article; zbMATH DE number 6701686
scientific article