Complex hyperbolic triangle groups of type [𝑚,𝑚,0;3,3,2

Abstract

In this paper we study discreteness of complex hyperbolic triangle groups of type [ m , m , 0 ; 3 , 3 , 2 ] [m,m,0;3,3,2] , i.e., groups of isometries of the complex hyperbolic plane generated by three complex reflections of orders 3 , 3 , 2 3,3,2 in complex geodesics with pairwise distances m , m , 0 m,m,0 . For fixed m m , the parameter space of such groups is of real dimension one. We determine intervals in this parameter space that correspond to discrete and to non-discrete triangle groups.