Falbel, Elisha; Parker, John R. The moduli space of the modular group in complex hyperbolic geometry. (English) Zbl 1160.32306 Invent. Math. 152, No. 1, 57-88 (2003). 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. Cited in 1 ReviewCited in 10 Documents MSC: 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds 20H10 Fuchsian groups and their generalizations (group-theoretic aspects) PDFBibTeX XMLCite \textit{E. Falbel} and \textit{J. R. Parker}, Invent. Math. 152, No. 1, 57--88 (2003; Zbl 1160.32306) Full Text: DOI