Schottky groups cannot act on $\mathbb{P}^{2n}_{\mathbb{C}}$ as subgroups of $PSL(2n+1,\Bbb{C})$

Abstract

In this paper we look at a special type of discrete subgroups of $PSL_{n+1}(\Bbb{C})$ called Schottky groups. We develop some basic properties of these groups and their limit set when $n > 1$, and we prove that Schottky groups only occur in odd dimensions, {\it i.e.}, they cannot be realized as subgroups of $PSL_{2n+1}(\Bbb{C})$.