Schottky groups acting on homogeneous rational 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.
Cite
@article{arxiv.1510.01076,
title = {Schottky groups acting on homogeneous rational manifolds},
author = {Christian Miebach and Karl Oeljeklaus},
journal= {arXiv preprint arXiv:1510.01076},
year = {2019}
}
Comments
30 pages; minor modifications, references have been added; to appear in Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal)