On the geometry of a Picard modular group
Martin Deraux
Université Grenoble Alpes, Gières, France
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Abstract
We study geometric properties of the action on the complex hyperbolic plane of the Picard modular group , where denotes the ring of algebraic integers in . We list conjugacy classes of maximal finite subgroups in and give an explicit description of the Fuchsian subgroups that occur as stabilizers of mirrors of complex reflections in . As an application, we describe an explicit torsion-free subgroup of index in .
Cite this article
Martin Deraux, On the geometry of a Picard modular group. Groups Geom. Dyn. 17 (2023), no. 4, pp. 1393–1416
DOI 10.4171/GGD/734