A relative Hilbert-Mumford criterion

Research output: Contribution to journalJournal articlepeer-review

  • 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.
Translated title of the contributionA relative Hilbert-Mumford criterion
Original languageEnglish
JournalManuscripta Mathematica
Volume148
Issue number3
Pages (from-to)283-301
ISSN0025-2611
DOIs
Publication statusPublished - 2015

    Research areas

  • math.AG, 14L24 (Primary) 13A50, 14D06 (Secondary)

ID: 130020451