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

Part of: Compact analytic spaces Complex manifolds

Published online by Cambridge University Press:  12 December 2014

Laurent Battisti  and
Karl Oeljeklaus
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

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.

Keywords

compact complex manifoldsalgebraic dimensionCousin groupslocally conformally Kähler manifolds

MSC classification

Primary: 32J18: Compact $n$-folds
Secondary: 32Q57: Classification theorems 32J99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 2 , June 2015 , pp. 273 - 285
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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