1997/12/19 by Peter Heinzner, Heinzner, Peter, Luca Migliorini +1
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Graph theory and applications #Homotopy and Cohomology in Algebraic Topology #alg-geom #dg-ga #math.AG #math.DG
paper · pdf · doi:10.48550/arxiv.dg-ga/9712008
19 pages, plain-tex
arxiv created 1997/12/19 · openalex publication_date 1997/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.