2010/10/14 by Daniel Greb, Christian Miebach
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Complex manifold #Computer science #Embedding #Equivariant map #Geometry and complex manifolds #Group theory #Holomorphic function #Invariant (physics) #Lie group #Mathematics #Meromorphic function #Pure mathematics #Reductive group #Stein manifold #math.CV #msc:14L30 #msc:22E46 #msc:32A20 #msc:32M05 #msc:32Q28
paper · pdf · doi:10.5802/aif.2740
published as Ann. Inst. Fourier (Grenoble) 62 (2012), no. 5, 1983-2011 · 20 pages, 1 figure
arxiv created 2010/10/14 · openalex publication_date 2012/01/01 · arxiv updated 2015/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we develop fundamental tools and methods to study meromorphic functions in an equivariant setup. As our main result we construct quotients of Rosenlicht-type for Stein spaces acted upon holomorphically by complex-reductive Lie groups and their algebraic subgroups. In particular, we show that in this setup invariant meromorphic functions separate orbits in general position. Applications to almost homogeneous spaces and principal orbit types are given. Furthermore, we use the main result to investigate the relation between holomorphic and meromorphic invariants for reductive group actions. As one important step in our proof we obtain a weak equivariant analogue of Narasimhan’s embedding theorem for Stein spaces.