On modality and complexity of affine embeddings
Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1133-1138 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $G$ be a reductive algebraic group and let $H$ be a reductive subgroup of $G$. The modality of a $G$-variety $X$ is the largest number of the parameters in a continuous family of $G$-orbits in $X$. A precise formula for the maximum value of the modality over all affine embeddings of the homogeneous space $G/H$ is obtained.
@article{SM_2001_192_8_a1,
     author = {I. V. Arzhantsev},
     title = {On modality and complexity of affine embeddings},
     journal = {Sbornik. Mathematics},
     pages = {1133--1138},
     year = {2001},
     volume = {192},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_8_a1/}
}
TY  - JOUR
AU  - I. V. Arzhantsev
TI  - On modality and complexity of affine embeddings
JO  - Sbornik. Mathematics
PY  - 2001
SP  - 1133
EP  - 1138
VL  - 192
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_2001_192_8_a1/
LA  - en
ID  - SM_2001_192_8_a1
ER  - 
%0 Journal Article
%A I. V. Arzhantsev
%T On modality and complexity of affine embeddings
%J Sbornik. Mathematics
%D 2001
%P 1133-1138
%V 192
%N 8
%U http://geodesic.mathdoc.fr/item/SM_2001_192_8_a1/
%G en
%F SM_2001_192_8_a1
I. V. Arzhantsev. On modality and complexity of affine embeddings. Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1133-1138. http://geodesic.mathdoc.fr/item/SM_2001_192_8_a1/

[1] Vinberg E. B., Popov V. L., “Teoriya invariantov”, Itogi nauki i tekhniki. Sovr. probl. matem. Fundam. napravleniya, 55, VINITI, M., 1989, 137–309 | MR

[2] Sukhanov A. A., “Opisanie nablyudaemykh podgrupp lineinykh algebraicheskikh grupp”, Matem. sb., 137 (179):1 (1988), 90–102 | MR | Zbl

[3] Luna D., “Slices étales”, Mém. Soc. Math. France (N. S.), 33 (1973), 81–105 | MR | Zbl

[4] Luna D., “Adhérences d'orbite et invariants”, Invent. Math., 29 (1975), 231–238 | DOI | MR | Zbl

[5] Arzhantsev I. V., Timashev D. A., “Affine embeddings with a finite number of orbits”, Transformation groups, 6:2 (2001), 101–110 | DOI | MR | Zbl

[6] Akhiezer D. N., “O modalnosti i slozhnosti deistvii reduktivnykh grupp”, UMN, 43:2 (1988), 129–130 | MR | Zbl

[7] Vinberg E. B., “Slozhnost deistvii reduktivnykh grupp”, Funkts. analiz i ego pril., 20:1 (1986), 1–13 | MR | Zbl

[8] Luna D., Vust Th., “Plongements d'espaces homogènes”, Comment. Math. Helv., 58 (1983), 186–245 | DOI | MR | Zbl

[9] Bialynicki-Birula A., Hochschild G., Mostow G. D., “Extensions of representations of algebraic linear groups”, Amer. J. Math., 85 (1963), 131–144 | DOI | MR | Zbl

[10] Knop F., “Über Bewertungen, welche unter einer reduktiven Gruppe invariant sind”, Math. Ann., 295 (1993), 333–363 | DOI | MR | Zbl

[11] Knop F., “The asymptotic behavior of invariant collective motion”, Invent. Math., 116 (1994), 309–328 | DOI | MR | Zbl