2014/04/30 by Martin G. Gulbrandsen, Lars H. Halle, Klaus Hulek · 7 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic geometry #Field (mathematics) #Geometry and complex manifolds #Group (periodic table) #Moduli #Morphism #Noetherian #Number theory #math.AG #msc:13A50 #msc:14D06 #msc:14L24
paper · pdf · doi:10.1007/s00229-015-0744-8
published in manuscripta mathematica 148(3-4), 283-301 (Springer Science+Business Media) · v4: minor corrections
arxiv created 2015/03/09 · openalex publication_date 2015/03/24 · arxiv updated 2015/03/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We generalize the classical Hilbert-Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism X -> Spec A to a noetherian k-algebra A. We also extend the classical projectivity result for GIT quotients: the induced morphism Xss/G -> Spec AG is projective. As an example of applications to moduli problems, we consider degenerations of Hilbert schemes of points.