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arXiv · 1510.01076

Schottky groups acting on homogeneous rational manifolds

Christian Miebach·Karl Oeljeklaus
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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-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 SL(2,C)/Γfor Γa discrete free loxodromic subgroup of SL(2,C), previously obtained by A. Guillot.

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Christian Miebach, Karl Oeljeklaus. 2016-11-04. Schottky groups acting on homogeneous rational manifolds. https://doi.org/10.1515/crelle-2016-0065

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