A relative Hilbert-Mumford criterion

Martin G. Gulbrandsen; Lars Halvard Halle; Klaus Hulek

doi:10.1007/s00229-015-0744-8

A relative Hilbert-Mumford criterion

Bidragets oversatte titel: A relative Hilbert-Mumford criterion

Martin G. Gulbrandsen, Lars Halvard Halle, Klaus Hulek

Institut for Matematiske Fag

6 Citationer (Scopus)

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.

Bidragets oversatte titel	A relative Hilbert-Mumford criterion
Originalsprog	Engelsk
Tidsskrift	Manuscripta Mathematica
Vol/bind	148
Udgave nummer	3
Sider (fra-til)	283-301
ISSN	0025-2611
DOI	https://doi.org/10.1007/s00229-015-0744-8
Status	Udgivet - 1 nov. 2015

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10.1007/s00229-015-0744-8

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A relative Hilbert-Mumford criterion

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