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2 results

Holomorphic Line Bundles Over Domains in Cousin Groups and the Algebraic Dimension of Oeljeklaus-Toma Manifolds
Part of
- Compact analytic spaces
- Complex manifolds
Laurent Battisti, Karl Oeljeklaus
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 58 / Issue 2 / June 2015

Published online by Cambridge University Press:

12 December 2014, pp. 273-285
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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.

Effective Actions of the Unitary Group on Complex Manifolds
A. V. Isaev, N. G. Kruzhilin
Journal:

Canadian Journal of Mathematics / Volume 54 / Issue 6 / 01 December 2002

Published online by Cambridge University Press:

20 November 2018, pp. 1254-1279

Print publication:

01 December 2002
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We classify all connected $n$-dimensional complex manifolds admitting effective actions of the unitary group ${{U}_{n}}$ by biholomorphic transformations. One consequence of this classification is a characterization of ${{\mathbb{C}}^{n}}$ by its automorphism group.