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Kählerian extensions of the symplectic reduction. (English) Zbl 0803.53042
The existence of a Kählerian Stein extension of a symplectic manifold is proved. It is shown that the symplectic structure on the reduction of the moment fiber is induced by the natural Kählerian quotient structure. A general context for studying singular symplectic structures via plurisubharmonic functions on Stein spaces is proposed.
Reviewer: P.Heinzner

MSC:
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
32U05 Plurisubharmonic functions and generalizations
32F10 \(q\)-convexity, \(q\)-concavity
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