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Levi's Problem for Pseudoconvex Homogeneous Manifolds
Published online by Cambridge University Press: 20 November 2018
Abstract
Suppose $G$ is a connected complex Lie group and
$H$ is a closed complex subgroup. Then there exists a closed complex subgroup
$J$ of
$G$ containing
$H$ such that the fibration
$\pi :G/H\to $
$G/J$ is the holomorphic reduction of
$G/H$i.e.,
$G/J$ is holomorphically separable and
$\mathcal{O}(G/H)\cong $
${{\pi }^{*}}\mathcal{O}(G/J)$. In this paper we prove that if
$G/H$ is pseudoconvex, i.e., if
$G/H$ admits a continuous plurisubharmonic exhaustion function, then
$G/J$ is Stein and
$J/H$ has no non-constant holomorphic functions.
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- © Canadian Mathematical Society 2017 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- Copyright © Canadian Mathematical Society 2017
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