On the structure of complex solvmanifolds (Q1089477)

A connected complex space X is called a solvmanifold if there is a connected complex solvable Lie group G which acts holomorphically and transitively on it. The aim of the paper is to study two classes of solvmanifolds: i) X is Kähler, ii) X is separable by analytic hypersurfaces. Main Theorem: Let X be a complex solvmanifold which satisfies i) or ii) and let \(\pi\) : \(X\to ^{F}Y\) be the holomorphic reduction of X. Then Y is a Stein manifold and F is an abelian complex Liegroup with \({\mathcal O}(F)\cong {\mathbb{C}}\). Moreover the fundamental group \(\pi _ 1(X)\) contains a nilpotent subgroup of finite index. As an application a conjecture of D. N. Ahiezer on hypersurfaces in complex Lie groups is proved in the solvable case.