Kählerian structures on symplectic reductions. (English) Zbl 0999.32011

Heinzner, Peter; Huckleberry, Alan

Peternell, Thomas (ed.) et al., Complex analysis and algebraic geometry. A volume in memory of Michael Schneider. Berlin: Walter de Gruyter. 225-253 (2000).

This largely expository paper, here cited by [*], by well-known experts in its topics, treats quotients and reduction of complex spaces, and appears as a chapter in a memorial volume dedicated to Michael Schneider, a well-known and influential contributor to complex geometry, whose life was cut short by a tragic accident. For another volume in memory of M. Schneider see [M. Schneider and Y.-T. Sin (eds.), Several Complex Variables (Berkeley, CA, 1995-1996), Math. Sci. Res. Inst. Publ. 37, Cambridge Univ. Press, Cambridge (1999; Zbl 0933.00014)], which has a chapter by the same authors also on holomorphic quotients [P. Heinzner and A. Huckleberry, Math. Sci. Res. Inst. Publ. 37, 309-349 (1999; Zbl 0959.32013)]. The paper [*] gives an exposition (aimed also at the non-specialist) of quotient theory for holomorphic actions of reductive groups on complex spaces; a theory useful in many mathematical and physical settings.
For the entire collection see [Zbl 0933.00031].

Reviewer: Imre Patyi (Irvine)

MSC:

32M05	Complex Lie groups, group actions on complex spaces
14L24	Geometric invariant theory
53D20	Momentum maps; symplectic reduction

Keywords:

complex Lie groups; geometric invariant theory; momentum maps; symplectic reduction

Citations:

Zbl 0933.00031; Zbl 0933.00014; Zbl 0959.32013