Schottky groups acting on homogeneous rational manifolds

TL;DR

This paper explores Schottky group actions on homogeneous rational manifolds, discovering new families and analyzing their complex geometric properties, thereby expanding the understanding of non-Kähler compact complex manifolds with free fundamental groups.

Contribution

It introduces two new families of Schottky group actions on homogeneous rational manifolds, extending known constructions and analyzing their geometric and analytic invariants.

Findings

Found two new families of Schottky group actions

Constructed examples of non-Kähler compact complex manifolds with free fundamental groups

Extended results on geometric invariants of these manifolds

Abstract

We systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori's well-known construction. This yields new examples of non-K\"ahler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to L\'arusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of SL(2,C)/\Gamma for \Gamma a discrete free loxodromic subgroup of SL(2,C), previously obtained by A. Guillot.