A general Hilbert-Mumford criterion
Annales de l'Institut Fourier, Volume 53 (2003) no. 3, p. 701-712
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.
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.
DOI : https://doi.org/10.5802/aif.1956
Classification:  14L24,  14L30
Keywords: reductive group actions, good quotients
@article{AIF_2003__53_3_701_0,
     author = {Hausen, J\"urgen},
     title = {A general Hilbert-Mumford criterion},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {3},
     year = {2003},
     pages = {701-712},
     doi = {10.5802/aif.1956},
     mrnumber = {2008437},
     zbl = {1044.14020},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2003__53_3_701_0}
}
Hausen, Jürgen. A general Hilbert-Mumford criterion. Annales de l'Institut Fourier, Volume 53 (2003) no. 3, pp. 701-712. doi : 10.5802/aif.1956. https://aif.centre-mersenne.org/item/AIF_2003__53_3_701_0/

[1] A. Białynicki-Birula; V.L. Popov Eds. Algebraic Quotients, R.V. Gamkrelidze (Encyclopedia of Mathematical Sciences) Tome Vol. 131 (2002), pp. 1-82 | Zbl 1061.14046

[2] A. Białynicki-Birula; J. Świȩcicka Generalized moment functions and orbit spaces, Amer. J. Math, Tome Vol. 109 (1987), pp. 229-238 | Article | Zbl 0624.14009

[3] A. Białynicki-Birula; J. Świȩcicka A reduction theorem for existence of good quotients, Amer. J. Math, Tome Vol. 113 (1990), pp. 189-201 | Article | Zbl 0741.14031

[4] A. Białynicki-Birula; J. Świȩcicka On complete orbit spaces of S L ( 2 ) -actions, Colloq. Math, Tome Vol. 55 (1988) no. 2, pp. 229-241 | Zbl 0682.14034

[5] A. Białynicki-Birula; J. Świȩcicka On complete orbit spaces of S L ( 2 ) -actions II, Colloq. Math, Tome Vol. 63 (1992) no. 1, pp. 9-20 | Zbl 0813.14032

[6] A. Białynicki-Birula; J. Świȩcicka Open subsets of projective spaces with a good quotient by an action of a reductive group, Transform. Groups, Tome Vol. 1 (1996) no. 3, pp. 153-185 | Article | Zbl 0912.14016

[7] A. Białynicki-Birula; J. Świȩcicka Three theorems on existence of good quotients, Math. Ann, Tome 307 (1997), pp. 143-149 | Article | Zbl 0870.14034

[8] D. Birkes Orbits of linear algebraic groups, Ann. Math., Ser. 2, Tome 93 (1971), pp. 459-475 | Article | MR 296077 | Zbl 0198.35001

[9] D. Cox The homogeneous coordinate ring of a toric variety, J. Algebr. Geom, Tome Vol. 4 (1995) no. 1, pp. 17-50 | MR 1299003 | Zbl 0846.14032

[10] J. Hausen Equivariant embeddings into smooth toric varieties, Canad. Math. J, Tome Vol. 54 (2002) no. 3, pp. 554-570 | Article | MR 1900763 | Zbl 1055.14014

[11] J. Hausen Producing good quotients by embedding into toric varieties, SMF (Sémin. et Congrès) Tome 6 (2002), pp. 193-212 | Zbl 1050.14045

[12] J. Hausen A Hilbert-Mumford Criterion for S L 2 -actions (to appear in Colloq. Math.) | MR 2031843 | Zbl 1054.14060

[13] J. Świȩcicka Quotients of toric varieties by actions of subtori, Colloq. Math, Tome 82 (1999) no. 1, pp. 105-116 | MR 1736038 | Zbl 0961.14032

[14] J. Świȩcicka A combinatorial construction of sets with good quotients by an action of a reductive group, Colloq. Math, Tome 87 (2001) no. 1, pp. 85-102 | Article | MR 1812145 | Zbl 0963.14020

[15] J. W\Lodarczyk Embeddings in toric varieties and prevarieties, J. Algebr. Geom, Tome 2 (1993) no. 4, pp. 705-726 | MR 1227474 | Zbl 0809.14043