Complex Hyperbolic Triangle Groups of Type $[m,m,0;n_1,n_2,2]$

Abstract

In this paper we study the discreteness of complex hyperbolic triangle groups of type $[m,m,0;n_1,n_2,2]$, i.e. groups of isometries of the complex hyperbolic plane generated by three complex reflections of orders $n_1,n_2,2$ 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 $n_1$ and $n_2$ and also intervals in the parameter space that correspond to discrete and non-discrete triangle groups.

34 pages, 2 figures. arXiv admin note: text overlap with arXiv:1901.01572