Holomorphic line bundles over domains in Cousin groups and the algebraic dimension of OT-manifolds

TL;DR

This paper extends the understanding of holomorphic line bundles over domains in Cousin groups and demonstrates that OT-manifolds have algebraic dimension zero, with implications for their irregularity.

Contribution

It generalizes Vogt's results to domains stable under maximal compact subgroups and proves OT-manifolds have algebraic dimension zero.

Findings

OT-manifolds have algebraic dimension zero

Certain Cousin groups have finite-dimensional irregularity

Extension of line bundle results to new classes of domains

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 in the sequel to show that the algebraic dimension of OT-manifolds is zero. In the last part we establish that certain Cousin groups, in particular those arising from the construction of OT-manifolds, have finite-dimensional irregularity.