Paper detail

The limit set of discrete subgroups of $PSL(3,\C)$

If $Γ$ is a discrete subgroup of $PSL(3,\Bbb{C})$, it is determined the equicontinuity region $Eq(Γ)$ of the natural action of $Γ$ on $\Bbb{P}^2_\Bbb{C}$. It is also proved that the action restricted to $Eq(Γ)$ is discontinuous, and $Eq(Γ)$ agrees with the discontinuity set in the sense of Kulkarni whenever the limit set of $Γ$ in the sense of Kulkarni, $Λ(Γ)$, contains at least three lines in general position. Under some additional hypothesis, it turns out to be the largest open set on which $Γ$ acts discontinuously. Moreover, if $Λ(Γ)$ contains at least four complex lines and $Γ$ acts on $\Bbb{P}^2_\Bbb{C}$ without fixed points nor invariant lines, then each connected component of $Eq(Γ)$ is a holomorphy domain and a complete Kobayashi hyperbolic space.