Two-dimensional Veronese groups with an invariant ball

Abstract

Abstract. In this article we characterize the complex hyperbolic groups that leave invariant a copy of the Veronese curve in P 2 C . As a corollary we get that every discrete compact surface group in PO + (2, 1) admits a deformation in PSL(3, 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 P 2 C , see [4,6,[13][14][15].

Exceptional Algebraic sets for discrete groups of $PSL(3,\Bbb{C})$

“…In the case of discrete groups preserving the Veronese group the Kulkarni limit set is the set of lines tangent to the Veronese group at points to the curve at points of the usual limit set of the action restricted to the curve, see [4]. For groups preserving the Curve the limit set is not hard to check that its Kulkarni limit set consist of two lines.…”