Geodesic
Contractions of affine spherical varieties
Sbornik. Mathematics, Tome 190 (1999) no. 7, pp. 937-954 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The language of filtrations and contractions is used to describe the class of $G$-varieties obtainable as the total spaces of the construction of contraction applied to affine spherical varieties, which is well-known in invariant theory. These varieties are local models for arbitrary affine $G$-varieties of complexity 1 with a one-dimensional categorical quotient. As examples, reductive algebraic semigroups and three-dimensional $\operatorname{SL}_2$-varieties are considered. 
@article{SM_1999_190_7_a0,
     author = {I. V. Arzhantsev},
     title = {Contractions of affine spherical varieties},
     journal = {Sbornik. Mathematics},
     pages = {937--954},
     year = {1999},
     volume = {190},
     number = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_7_a0/}
}
TY  - JOUR
AU  - I. V. Arzhantsev
TI  - Contractions of affine spherical varieties
JO  - Sbornik. Mathematics
PY  - 1999
SP  - 937
EP  - 954
VL  - 190
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/SM_1999_190_7_a0/
LA  - en
ID  - SM_1999_190_7_a0
ER  - 
%0 Journal Article
%A I. V. Arzhantsev
%T Contractions of affine spherical varieties
%J Sbornik. Mathematics
%D 1999
%P 937-954
%V 190
%N 7
%U http://geodesic.mathdoc.fr/item/SM_1999_190_7_a0/
%G en
%F SM_1999_190_7_a0
I. V. Arzhantsev. Contractions of affine spherical varieties. Sbornik. Mathematics, Tome 190 (1999) no. 7, pp. 937-954. http://geodesic.mathdoc.fr/item/SM_1999_190_7_a0/

[1] Popov V. L., “Styagivanie deistvii reduktivnykh algebraicheskikh grupp”, Matem. sb., 130(172):3(7) (1986), 310–334 | MR | Zbl

[2] Arzhantsev I. V., “O deistviyakh reduktivnykh grupp s odnoparametricheskim semeistvom sfericheskikh orbit”, Matem. sb., 188:5 (1997), 3–20 | MR | Zbl

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

[4] Vinberg E. B., Popov V. L., “Ob odnom klasse kvaziodnorodnykh affinnykh mnogoobrazii”, Izv. AN SSSR. Ser. matem., 36:4 (1972), 749–764 | MR | Zbl

[5] Popov V. L., “Kvaziodnorodnye affinnye algebraicheskie mnogoobraziya gruppy $\operatorname{SL}(2)$”, Izv. AN SSSR. Ser. matem., 37:4 (1973), 792–832 | MR | Zbl

[6] Vinberg E. B., “On reductive algebraic semigroups”, Amer. Math. Soc. Transl. Ser. 2, 169 (1995), 145–182 | MR | Zbl

[7] Kraft Kh., Geometricheskie metody v teorii invariantov, Mir, M., 1987 | MR | Zbl

[8] Danilov V. I., “Geometriya toricheskikh mnogoobrazii”, UMN, 33:2 (1978), 85–134 | MR | Zbl

[9] Vinberg E. B., Popov V. L., “Teoriya invariantov”, Itogi nauki i tekhn. Sovr. probl. matem. Fundam. napr., 55, VINITI, M., 1989, 137–314 | MR

[10] Arzhantsev I. V., “O deistviyakh slozhnosti odin gruppy $\operatorname{SL}_2$”, Izv. RAN. Ser. matem., 61:4 (1997), 3–18 | MR | Zbl

[11] Arzhantsev I. V., “O normalnosti zamykanii sfericheskikh orbit”, Funkts. analiz i ego prilozh., 31:4 (1997), 66–69 | MR | Zbl