Two dimensional Veronese groups with an invariant ball

Abstract: In this article we characterize the complex hyperbolic groups that leave invariant a copy of the Veronese curve in $\Bbb{P}<sup>2_{\Bbb{C}}$. As a corollary we get that every discrete compact surface group in $\PO<sup>+(2,1)$ admits a deformation in $\PSL(3,\Bbb{C})$ with a non-empty region of discontinuity which is not conjugate to a complex hyperbolic subgroup. This provides a way to construct new examples of Kleinian groups acting on $\Bbb{P}<sup>2_\Bbb{C}$.