Levi's Problem for Pseudoconvex Homogeneous Manifolds

Gilligan, Bruce

Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 736-746

Résumé

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.

Détail

DOI : 10.4153/CMB-2017-007-x

Mots-clés : 32M10, 32U10, 32A10, 32Q28, complex homogeneous manifold, plurisubharmonic exhaustion function, holomorphic reduction, Stein manifold, Remmert reduction, Hirschowitz annihilator