A relative Hilbert-Mumford criterion
Algebraic Geometry
2015-03-31 v4
Abstract
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.
Cite
@article{arxiv.1404.7267,
title = {A relative Hilbert-Mumford criterion},
author = {Martin G. Gulbrandsen and Lars H. Halle and Klaus Hulek},
journal= {arXiv preprint arXiv:1404.7267},
year = {2015}
}
Comments
v4: minor corrections