Gulbrandsen, Martin G.4; Halle, Lars Halvard5; Hulek, Klaus3
1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 University of Stavanger3 Leibniz Universität Hannover4 University of Stavanger5 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
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 X^ss/G -> Spec A^G is projective. As an example of applications to moduli problems, we consider degenerations of Hilbert schemes of points.
Manuscripta Mathematica, 2015, Vol 148, Issue 3, p. 283-301