AbstractWe 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-Kähler 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 Lárusson and to Seade
and Verjovsky. As a byproduct, we see that the Schottky construction allows to
recover examples of equivariant compactifications of
{{\rm{SL}}(2,\mathbb{C})/\Gamma} for Γ a discrete free loxodromic subgroup
of {{\rm{SL}}(2,\mathbb{C})}, previously obtained by A. Guillot.
Schottky groups acting on homogeneous rational manifolds
