A relative Hilbert-Mumford criterion

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Standard

A relative Hilbert-Mumford criterion. / Gulbrandsen, Martin G.; Halle, Lars Halvard; Hulek, Klaus.

I: Manuscripta Mathematica, Bind 148, Nr. 3, 2015, s. 283-301.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Gulbrandsen, MG, Halle, LH & Hulek, K 2015, 'A relative Hilbert-Mumford criterion', Manuscripta Mathematica, bind 148, nr. 3, s. 283-301. https://doi.org/10.1007/s00229-015-0744-8

APA

Gulbrandsen, M. G., Halle, L. H., & Hulek, K. (2015). A relative Hilbert-Mumford criterion. Manuscripta Mathematica, 148(3), 283-301. https://doi.org/10.1007/s00229-015-0744-8

Vancouver

Gulbrandsen MG, Halle LH, Hulek K. A relative Hilbert-Mumford criterion. Manuscripta Mathematica. 2015;148(3):283-301. https://doi.org/10.1007/s00229-015-0744-8

Author

Gulbrandsen, Martin G. ; Halle, Lars Halvard ; Hulek, Klaus. / A relative Hilbert-Mumford criterion. I: Manuscripta Mathematica. 2015 ; Bind 148, Nr. 3. s. 283-301.

Bibtex

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title = "A relative Hilbert-Mumford criterion",
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.",
keywords = "math.AG, 14L24 (Primary) 13A50, 14D06 (Secondary)",
author = "Gulbrandsen, {Martin G.} and Halle, {Lars Halvard} and Klaus Hulek",
note = "v3: introduction rewritten, reference added",
year = "2015",
doi = "10.1007/s00229-015-0744-8",
language = "English",
volume = "148",
pages = "283--301",
journal = "Manuscripta Mathematica",
issn = "0025-2611",
publisher = "Springer",
number = "3",

}

RIS

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