On the number of lines in the limit set for discrete subgroups of $PSL(3,\Bbb{C})$

Abstract

Given a discret subgroup $Γ\subset PSL(3,\C)$, we determine the number of complex lines and complex lines in general position lying in the complement of: maximal regions on which $Γ$ acts properly discontinuously, the Kularni's limit set of $Γ$ and the equicontinuity set of $Γ$. We also provide sufficient conditions to ensure that the equicontinuity region agrees with the Kulkarni's discontinuity region and is the largest set where the group acts properly discontinuously and we provide a description of he respective limit set in terms of the elements of the group.