Kählerian extensions of the symplectic reduction. (English) Zbl 0803.53042

Heinzner, P.; Huckleberry, A. T.; Loose, F.

J. Reine Angew. Math. 455, 123-140 (1994).

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

Keywords:

Kählerian Stein extension; symplectic manifold; Kählerian quotient; singular symplectic structures; plurisubharmonic functions