Geodesic
On the birational classification of algebraic group actions
Izvestiya. Mathematics , Tome 65 (2001) no. 1, pp. 57-70.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we show that, in a number of cases, the birational classification of some actions of an arbitrary algebraic group can be reduced to the birational classification of locally free actions of reductive groups. We prove the existence of ordinary and relative sections for some actions 
@article{IM2_2001_65_1_a2,
     author = {V. \'E. Kordonskii},
     title = {On the birational classification of algebraic group actions},
     journal = {Izvestiya. Mathematics },
     pages = {57--70},
     publisher = {mathdoc},
     volume = {65},
     number = {1},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2001_65_1_a2/}
}
TY  - JOUR
AU  - V. É. Kordonskii
TI  - On the birational classification of algebraic group actions
JO  - Izvestiya. Mathematics 
PY  - 2001
SP  - 57
EP  - 70
VL  - 65
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2001_65_1_a2/
LA  - en
ID  - IM2_2001_65_1_a2
ER  - 
%0 Journal Article
%A V. É. Kordonskii
%T On the birational classification of algebraic group actions
%J Izvestiya. Mathematics 
%D 2001
%P 57-70
%V 65
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2001_65_1_a2/
%G en
%F IM2_2001_65_1_a2
V. É. Kordonskii. On the birational classification of algebraic group actions. Izvestiya. Mathematics , Tome 65 (2001) no. 1, pp. 57-70. http://geodesic.mathdoc.fr/item/IM2_2001_65_1_a2/

[1] Veisfeiler B. Yu., “Ob odnom klasse unipotentnykh podgrupp poluprostykh algebraicheskikh grupp”, UMN, 21:2 (1966), 222–223 | MR

[2] Vinberg E. B., Onischik A. L., Seminar po gruppam Li i algebraicheskim gruppam, Nauka, M., 1988 | MR

[3] Vinberg E. B., Popov V. L., “Teoriya invariantov”, Itogi nauki i tekhn. Sovrem. probl. matem. Fundam. napravl., 55, VINITI, M., 1989, 137–309 | MR

[4] Katsylo P. I., “Ratsionalnost prostranstv modulei giperellipticheskikh krivykh”, Izv. AN SSSR. Ser. matem., 48:4 (1984), 705–710 | MR | Zbl

[5] Morozov V. V., “Klassifikatsiya nilpotentnykh algebr Li 6-go poryadka”, Izv. vuzov. Matem., 1958, no. 4, 161–171 | MR | Zbl

[6] Platonov V. P., Rapinchuk A. S., Algebraicheskie gruppy i teoriya chisel, Nauka, M., 1991 | MR

[7] Serr Zh.-P., Kogomologii Galua, Mir, M., 1968 | MR

[8] Springer T. A., “Lineinye algebraicheskie gruppy”, Itogi nauki i tekhn. Sovrem. probl. matem. Fundam. napravl., 55, VINITI, M., 1989, 5–136 | MR

[9] Khamfri Dzh., Lineinye algebraicheskie gruppy, Nauka, M., 1980 | MR

[10] Kraft H., Schwarz G. W., “Reductive Group Actions with one-dimensional quotient”, Publ. Math. IHES, 76 (1992), 1–97 | MR | Zbl

[11] Lang S., “On quasi-algebraic clouser”, Ann. Math., 55 (1952), 373–390 | DOI | MR | Zbl

[12] Popov V. L., “Sections in Invariant Theory”, The Sophus Lie Memorial Conference, Proceedings (Oslo, 1992), Scandinavian University Press, 1994, 315–361 | MR

[13] Richardson R. U., “Deformations of Lie subgroups and the variation of isotropy subgroups”, Acta Math., 129:1–2 (1972), 35–73 | DOI | MR | Zbl

[14] Rosenlicht M., “Some basic theorems on algebraic groups”, Amer. J. Math., 178 (1956), 401–443 | DOI | MR

[15] Anneaux de Chow et applications, Séminaire C. Chevalley. 2nd année, IHP, 1958

[16] Serre J.-P., Cohomologie Galoisienne: Progrès et Problèms, Séminaire BOURBAKI. 46ème, année, no. 783, 1993–94 | MR

[17] Sansuc J. J., “Groupe de Brauer et arithmétique des groupes algébriques linéairessur un corps de nombers”, J. Reine Angew. Math., 327 (1981), 12–80 | MR | Zbl

[18] Vinberg E. B., “On invariants of a set of matrices”, J. of Lie Theory, 6 (1996), 249–269 | MR | Zbl