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

Abstract

AbstractIn 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.