On holomorphically separable complex solv-manifolds
Annales de l'Institut Fourier, Volume 36 (1986) no. 3, pp. 57-65.

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 H ^ of finite index in H with π 1 (G/H ^) nilpotent. In special situations (e.g. if H is discrete) H normalizes H ^ and H/H ^ is abelian.

Soit G un groupe de Lie complexe résoluble et H un sous-groupe complexe fermé de G. Si les fonctions holomorphes sur la variété complexe X:=G/H séparent localement les points de X, alors X est une variété de Stein. De plus, il existe un sous-groupe H ^ d’indice fini dans H avec π 1 (G/H) nilpotent. Dans des cas particuliers (par exemple si H est discret), H normalise H ^ et H/H ^ est abélien.

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     title = {On holomorphically separable complex solv-manifolds},
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Huckleberry, Alan T.; Oeljeklaus, E. On holomorphically separable complex solv-manifolds. Annales de l'Institut Fourier, Volume 36 (1986) no. 3, pp. 57-65. doi : 10.5802/aif.1059. http://archive.numdam.org/articles/10.5802/aif.1059/

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