×

The moduli space of the modular group in complex hyperbolic geometry. (English) Zbl 1160.32306

Summary: We construct the space of discrete, faithful, type-preserving representations of the modular group into the isometry group of complex hyperbolic 2-space up to conjugacy. This is the first Fuchsian group for which the entire complex hyperbolic deformation space has been constructed. We also show how the \(\mathbb C\)-spheres of Falbel-Zocca are related to the \(\mathbb R\)-spheres (hybrid spheres) of Schwartz.

MSC:

32Q45 Hyperbolic and Kobayashi hyperbolic manifolds
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
PDFBibTeX XMLCite
Full Text: DOI