Projectivity of moment map quotients

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
19 pages, plain-tex

Keywords

Differential Geometry, Algebraic Geometry

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/33400

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/dg-ga/9712008
 http://arxiv.org/abs/dg-ga/9712008

Collections

arXiv