Fundamental domains and generators for lattice Veech groups
type: Item
instance of: scholarly article
title: Fundamental domains and generators for lattice Veech groups
zbMATH Open document ID: 1362.32010
DOI: 10.4171/CMH/406
author: Ronen E. Mukamel
published in: Commentarii Mathematici Helvetici
publication date: 2017-04-05T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 30F30
zbMATH DE Number: 6701686
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: moduli space of quadratic differentials
zbMATH Keywords: Veech groups
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/cmh/406
OpenAlex ID: W2591086496
description: scientific article; zbMATH DE number 6701686