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

Abstract

In this paper we look at a special type of discrete subgroups of $PS{L}_{n+1}(\mathbb{C})$ 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 $PS{L}_{2n+1}(\mathbb{C})$.

9 pages. To appear in Bulletin of the Brazilian Mathematical Society. The original publication is available at http://www.springerlink.com