A general Hilbert-Mumford criterion
[Un critère de Hilbert-Mumford général]
Annales de l'Institut Fourier, Tome 53 (2003) no. 3, pp. 701-712.

Soit X une variété algébrique munie d’une action d’un groupe réductif G. On donne un critère à la Hilbert-Mumford pour la construction des ouverts G-stables VX admettant un bon quotient par g.

Let a reductive group G act on an algebraic variety X. We give a Hilbert-Mumford type criterion for the construction of open G-invariant subsets VX admitting a good quotient by G.

DOI : 10.5802/aif.1956
Classification : 14L24, 14L30
Keywords: reductive group actions, good quotients
Mot clés : actions des groupes réductifs, bons quotients
Hausen, Jürgen 1

1 Universität Konstanz, Fachbereich Mathematik und Statistik, Universitätstrasse 10, 78457 Konstanz (Allemagne)
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Hausen, Jürgen. A general Hilbert-Mumford criterion. Annales de l'Institut Fourier, Tome 53 (2003) no. 3, pp. 701-712. doi : 10.5802/aif.1956. http://archive.numdam.org/articles/10.5802/aif.1956/

[1] A. Białynicki-Birula; V.L. Popov Eds. Algebraic Quotients, R.V. Gamkrelidze (Encyclopedia of Mathematical Sciences), Volume Vol. 131 (2002), pp. 1-82 | Zbl

[2] A. Białynicki-Birula; J. Świȩcicka Generalized moment functions and orbit spaces, Amer. J. Math, Volume Vol. 109 (1987), pp. 229-238 | DOI | Zbl

[3] A. Białynicki-Birula; J. Świȩcicka A reduction theorem for existence of good quotients, Amer. J. Math, Volume Vol. 113 (1990), pp. 189-201 | DOI | Zbl

[4] A. Białynicki-Birula; J. Świȩcicka On complete orbit spaces of S L ( 2 ) -actions, Colloq. Math, Volume Vol. 55 (1988) no. 2, pp. 229-241 | Zbl

[5] A. Białynicki-Birula; J. Świȩcicka On complete orbit spaces of S L ( 2 ) -actions II, Colloq. Math, Volume Vol. 63 (1992) no. 1, pp. 9-20 | Zbl

[6] A. Białynicki-Birula; J. Świȩcicka Open subsets of projective spaces with a good quotient by an action of a reductive group, Transform. Groups, Volume Vol. 1 (1996) no. 3, pp. 153-185 | DOI | Zbl

[7] A. Białynicki-Birula; J. Świȩcicka Three theorems on existence of good quotients, Math. Ann, Volume 307 (1997), pp. 143-149 | DOI | Zbl

[8] D. Birkes Orbits of linear algebraic groups, Ann. Math., Ser. 2, Volume 93 (1971), pp. 459-475 | DOI | MR | Zbl

[9] D. Cox The homogeneous coordinate ring of a toric variety, J. Algebr. Geom, Volume Vol. 4 (1995) no. 1, pp. 17-50 | MR | Zbl

[10] J. Hausen Equivariant embeddings into smooth toric varieties, Canad. Math. J, Volume Vol. 54 (2002) no. 3, pp. 554-570 | DOI | MR | Zbl

[11] J. Hausen Producing good quotients by embedding into toric varieties (Sémin. et Congrès), Volume 6 (2002), pp. 193-212 | Zbl

[12] J. Hausen A Hilbert-Mumford Criterion for S L 2 -actions (to appear in Colloq. Math.) | MR | Zbl

[13] J. Świȩcicka Quotients of toric varieties by actions of subtori, Colloq. Math, Volume 82 (1999) no. 1, pp. 105-116 | MR | Zbl

[14] J. Świȩcicka A combinatorial construction of sets with good quotients by an action of a reductive group, Colloq. Math, Volume 87 (2001) no. 1, pp. 85-102 | DOI | MR | Zbl

[15] J. W\Lodarczyk Embeddings in toric varieties and prevarieties, J. Algebr. Geom, Volume 2 (1993) no. 4, pp. 705-726 | MR | Zbl

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