Let be a solvable complex Lie group and a closed complex subgroup of . If the global holomorphic functions of the complex manifold locally separate points on , then is a Stein manifold. Moreover there is a subgroup of finite index in with nilpotent. In special situations (e.g. if is discrete) normalizes and is abelian.
Soit un groupe de Lie complexe résoluble et un sous-groupe complexe fermé de . Si les fonctions holomorphes sur la variété complexe séparent localement les points de , alors est une variété de Stein. De plus, il existe un sous-groupe d’indice fini dans avec nilpotent. Dans des cas particuliers (par exemple si est discret), normalise et est abélien.
@article{AIF_1986__36_3_57_0, author = {Huckleberry, Alan T. and Oeljeklaus, E.}, title = {On holomorphically separable complex solv-manifolds}, journal = {Annales de l'Institut Fourier}, pages = {57--65}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {36}, number = {3}, year = {1986}, doi = {10.5802/aif.1059}, mrnumber = {88b:32069}, zbl = {0571.32012}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1059/} }
TY - JOUR AU - Huckleberry, Alan T. AU - Oeljeklaus, E. TI - On holomorphically separable complex solv-manifolds JO - Annales de l'Institut Fourier PY - 1986 SP - 57 EP - 65 VL - 36 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.1059/ DO - 10.5802/aif.1059 LA - en ID - AIF_1986__36_3_57_0 ER -
%0 Journal Article %A Huckleberry, Alan T. %A Oeljeklaus, E. %T On holomorphically separable complex solv-manifolds %J Annales de l'Institut Fourier %D 1986 %P 57-65 %V 36 %N 3 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.1059/ %R 10.5802/aif.1059 %G en %F AIF_1986__36_3_57_0
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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