A relative Hilbert-Mumford criterion
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A relative Hilbert-Mumford criterion. / Gulbrandsen, Martin G.; Halle, Lars Halvard; Hulek, Klaus.
In: Manuscripta Mathematica, Vol. 148, No. 3, 2015, p. 283-301.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - A relative Hilbert-Mumford criterion
AU - Gulbrandsen, Martin G.
AU - Halle, Lars Halvard
AU - Hulek, Klaus
N1 - v3: introduction rewritten, reference added
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - math.AG
KW - 14L24 (Primary) 13A50, 14D06 (Secondary)
U2 - 10.1007/s00229-015-0744-8
DO - 10.1007/s00229-015-0744-8
M3 - Journal article
VL - 148
SP - 283
EP - 301
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
SN - 0025-2611
IS - 3
ER -
ID: 130020451