Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-20T13:35:35.503Z Has data issue: false hasContentIssue false
  • English
  • Français

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, ([email protected])
Karl Oeljeklaus
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, CMI, 39 rue Frédéric Joliot-Curie, 13453 Marseille, France, ([email protected])
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Abe, Y. and Kopfermann, K., Toroidal groups: line bundles, cohomology and quasiabelian varieties, Lecture Notes in Mathematics, Volume 1759 (Springer, 2001).CrossRefGoogle Scholar
2.Berteloot, F. and Oeljeklaus, K., Invariant plurisubharmonic functions and hyper-surfaces on semisimple complex Lie groups, Math. Annalen 281(3) (1988), 513–530.CrossRefGoogle Scholar
3.Cousin, P., Sur les fonctions triplement périodiques de deux variables, Acta Math. 33(1) (1910), 105–232.CrossRefGoogle Scholar
4.Feldman, N. I. and Nesterenko, Yu. V., Number theory IV: transcendental numbers, Encyclopaedia of Mathematical Sciences, Volume 44 (Springer, 1998).Google Scholar
5.Gilligan, B., Miebach, C. and Oeljeklaus, K., Homogeneous Kähler and Hamiltonian manifolds, Math. Annalen 349(4) (2011), 889–901.CrossRefGoogle Scholar
6.Huckleberry, A. T. and Margulis, G. A., Invariant analytic hypersurfaces, Invent. Math. 71(1) (1983), 235–240.CrossRefGoogle Scholar
7.Oeljeklaus, K. and Toma, M., Non-Kähler compact complex manifolds associated to number fields, Annales Inst. Fourier 55(1) (2005), 161–171.CrossRefGoogle Scholar
8.Ornea, L. and Verbitsky, M., Oeljeklaus-Toma manifolds admitting no complex sub-varieties, Math. Res. Lett. 18(4) (2011), 747–754.CrossRefGoogle Scholar
9.Vogt, C., Line bundles on toroidal groups, J. Reine Angew. Math. 335 (1982), 197–215.Google Scholar
10.Vogt, C., Two remarks concerning toroidal groups, Manuscr. Math. 41(1) (1983), 217–232.CrossRefGoogle Scholar