A relative Hilbert-Mumford criterion

作者：Gulbrandsen Martin G; Halle Lars H; Hulek Klaus^*

来源：Manuscripta Mathematica, 2015, 148(3-4): 283-301.

DOI：10.1007/s00229-015-0744-8

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 to a noetherian k-algebra A. We also extend the classical projectivity result for GIT quotients: the induced morphism is projective. As an example of applications to moduli problems, we consider degenerations of Hilbert schemes of points.

• 出版日期2015-11