2016/07/31 by Bruce Gilligan
Mathematics · #Algebraic and Geometric Analysis #Fibration #Geometry and complex manifolds #Holomorphic and Operator Theory #Holomorphic function #Homogeneous #Lie group #Separable space #Stein manifold #math.CV #msc:32A10 #msc:32M10 #msc:32Q28 #msc:32U10
paper · pdf · doi:10.4153/cmb-2017-007-x
arguments in section 3 have been changed
openalex publication_date 2017/02/06 · openalex created_date 2017/02/17 · arxiv created 2017/08/02 · arxiv updated 2017/08/03 · openalex updated_date 2026/08/05
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 π:G/H ⟶ G/J is the holomorphic reduction of G/H; i.e., G/J is holomorphically separable and O( G/H )≅ π* 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.