A relative Hilbert-Mumford criterion
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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 contribution | A relative Hilbert-Mumford criterion |
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Original language | English |
Journal | Manuscripta Mathematica |
Volume | 148 |
Issue number | 3 |
Pages (from-to) | 283-301 |
ISSN | 0025-2611 |
DOIs | |
Publication status | Published - 2015 |
- math.AG, 14L24 (Primary) 13A50, 14D06 (Secondary)
Research areas
ID: 130020451