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Holomorphic Line Bundles Over Domains in Cousin Groups and the Algebraic Dimension of Oeljeklaus-Toma Manifolds

Published online by Cambridge University Press:  12 December 2014

Laurent Battisti
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, CMI, 39 rue Frédéric Joliot-Curie, 13453 Marseille, France, (karl.oeljeklaus@univ-amu.fr)
Karl Oeljeklaus
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, CMI, 39 rue Frédéric Joliot-Curie, 13453 Marseille, France, (karl.oeljeklaus@univ-amu.fr)
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Abstract

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In this paper we extend results due to Vogt on line bundles over Cousin groups to the case of domains stable by the maximal compact subgroup. This is used to show that the algebraic dimension of Oeljeklaus—Toma manifolds (OT-manifolds) is 0. In the last part we establish that certain Cousin groups, in particular those arising from the construction of OT-manifolds, have finite-dimensional irregularity.

Information

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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