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Daniel Greb; Christian Miebach
Invariant meromorphic functions on Stein spaces
(Fonctions méromorphes invariantes sur les espaces de Stein)
Annales de l'institut Fourier, 62 no. 5 (2012), p. 1983-2011, doi: 10.5802/aif.2740
Article PDF | Reviews MR 3025158 | Zbl 1270.32005
Class. Math.: 32M05, 32Q28, 32A20, 14L30, 22E46
Keywords: Lie group action, Stein space, invariant meromorphic function, Rosenlicht quotient

Résumé - Abstract

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.

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