Projectivity of moment map quotients

Details Projectivity of moment map quotients Projectivity of moment map quotients

1997-12-19

arxiv.org/abs/dg-ga/9712008v1

Mathematics

Algebraic Geometry

19 pages, plain-tex

Scientific paper

Let G be a complex reductive group and K a maximal compact subgroup. If X is a smooth projective G-variety, with a fixed (not necessarily integral) K-invariant Kaehler form, then the K-action is Hamiltonian. Let M be the zero fiber of the corresponding moment map. It is well known that the quotient M/K is a complex space in a natural way. We prove that M/K is a projective variety. In particular, it follows that semistability with respect to a moment map is equivalent to semistability in the sense of Mumford.

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