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Alan T. Huckleberry; E. Oeljeklaus
On holomorphically separable complex solv-manifolds
Annales de l'institut Fourier, 36 no. 3 (1986), p. 57-65, doi: 10.5802/aif.1059
Article PDF | Reviews MR 88b:32069 | Zbl 0571.32012 | 3 citations in Cedram

Résumé - Abstract

Let $G$ be a solvable complex Lie group and $H$ a closed complex subgroup of $G$. If the global holomorphic functions of the complex manifold $X:G/H$ locally separate points on $X$, then $X$ is a Stein manifold. Moreover there is a subgroup $\widehat{H}$ of finite index in $H$ with $\pi _1(G/\widehat{H})$ nilpotent. In special situations (e.g. if $H$ is discrete) $H$ normalizes $\widehat{H}$ and $H/\widehat{H}$ is abelian.

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