Complex hyperbolic triangle groups of type [m,m,0;n₁,n₂,2]

In this paper we study discreteness of complex hyperbolic triangle groups of type [m,m,0; n₁, n₂, 2] [ m , m , 0 ; n 1 , n 2 , 2 ] , i.e. groups of isometries of the complex hyperbolic plane generated by three complex reflections of orders n₁, n₂, 2 n 1 , n 2 , 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 n 1 and n₂ n 2 and also intervals in the parameter space that correspond to discrete and non-discrete triangle groups.