A relative Hilbert-Mumford criterion

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

  • Martin G. Gulbrandsen
  • Lars Halvard Halle
  • Klaus Hulek
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 titelA relative Hilbert-Mumford criterion
OriginalsprogEngelsk
TidsskriftManuscripta Mathematica
Vol/bind148
Udgave nummer3
Sider (fra-til)283-301
ISSN0025-2611
DOI
StatusUdgivet - 2015

Bibliografisk note

v3: introduction rewritten, reference added

ID: 130020451