Complex Hyperbolic Triangle Groups of Type [m,m,0; n1, n2, 2]
Abstract
In this paper we study the discreteness of complex hyperbolic triangle groups of type [m,m,0; n1, n2, 2], i.e. groups of isometries of the complex hyperbolic plane generated by three complex reflections of orders n1, n2, 2 in complex geodesics with pairwise distances m, m, 0. For fixed m, the parameter space of such groups is of real dimension one. We determine the possible orders for n1 and n2 and also intervals in the parameter space that correspond to discrete and non-discrete triangle groups.
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