Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

A minimal volume arithmetic cusped complex hyperbolic orbifold


a1 Institut de Mathématiques, Université Pierre et Marie Curie, 4, Place Jussieu, F-75252 Paris, France. e-mail:


The sister of Eisenstein–Picard modular group is described explicitly in [10], whose quotient is a noncompact arithmetic complex hyperbolic 2-orbifold of minimal volume (see [16]). We give a construction of a fundamental domain for this group. A presentation of that lattice can be obtained from that construction, which relates to one of Mostow's lattices.

(Received March 12 2010)

(Revised June 22 2010)

(Online publication October 08 2010)