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In this paper we study the discreteness of complex hyperbolic triangle groupsof type $[m,m,0; n_1, n_2, 2]$, i.e. groups of isometries of the complexhyperbolic plane generated by three complex reflections of orders $n_1, n_2, 2$in complex geodesics with pairwise distances $m, m, 0$. For fixed $m$, theparameter space of such groups is of real dimension one. We determine thepossible orders for $n_1$ and $n_2$ and also intervals in the parameter spacethat correspond to discrete and non-discrete triangle groups.

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