Geodesic
Classification of affine homogeneous spaces of complexity one
Sbornik. Mathematics, Tome 195 (2004) no. 6, pp. 765-782 Cet article a éte moissonné depuis la source Math-Net.Ru

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The complexity of an action of a reductive algebraic group $G$ on an algebraic variety $X$ is the codimension of a generic $B$-orbit in $X$, where $B$ is a Borel subgroup of $G$. Affine homogeneous spaces $G/H$ of complexity 1 are classified in this paper. These results are the natural continuation of the earlier classification of spherical affine homogeneous spaces, that is, spaces of complexity 0. 
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I. V. Arzhantsev; O. V. Chuvashova. Classification of affine homogeneous spaces of complexity one. Sbornik. Mathematics, Tome 195 (2004) no. 6, pp. 765-782. http://geodesic.mathdoc.fr/item/SM_2004_195_6_a0/

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

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

[3] Brion M., “Variétés sphériques”, Notes de la session de la S. M. F. “Opérations hamiltoniennes et opérations de groupes algébriques”, Grenoble, 1997; {http://www-fourier.ujf-grenoble.fr/m̃brion/spheriques.ps} {http://www-fourier.ujf-grenoble.fr/m̃brion/spheriques.ps}

[4] Knop F., “The Luna–Vust theory of spherical embeddings”, Proceeding of the Hyderabad conference on algebraic groups (Univ. Hyderabad, India, December 1989), eds. S. Ramanan, Manoj Prakashan, Madras, 1991, 225–249 | MR | Zbl

[5] Timashev D. A., “Klassifikatsiya $G$-mnogoobrazii slozhnosti 1”, Izv. RAN. Ser. matem., 61:2 (1997), 127–162 | MR | Zbl

[6] Akhiezer D. N., “O deistviyakh s konechnym chislom orbit”, Funkts. analiz i ego prilozh., 19:1 (1985), 1–5 | MR | Zbl

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

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

[9] Arzhantsev I. V., “O modalnosti i slozhnosti affinnykh vlozhenii”, Matem. sb., 192:8 (2001), 47–52 | MR | Zbl

[10] Mikityuk I. V., “Ob integriruemosti invariantnykh gamiltonovykh sistem s odnorodnymi konfiguratsionnymi prostranstvami”, Matem. sb., 129 (171) (1986), 514–534 | MR | Zbl

[11] Gullemin V., Sternberg S., “Multiplicity-free spaces”, J. Differential Geom., 19 (1984), 31–56 | MR

[12] Vinberg E. B., “Kommutativnye odnorodnye prostranstva i koizotropnye simplekticheskie deistviya”, UMN, 56:1 (2001), 3–62 | MR | Zbl

[13] Mykytyuk I. V., Stepin A. M., “Classification of almost spherical pairs of compact simple Lie groups”, Poisson geometry, Banach Center Publ., 51, eds. J. Grabowski, Polish Acad. Sci., Inst. Math., Warsawa, 2000, 231–241 | MR | Zbl

[14] Mykytyuk I. V., “Actions of Borel subgroups on homogeneous spaces of reductive complex Lie groups and integrability”, Compositio Math., 127 (2001), 55–67 | DOI | MR | Zbl

[15] Krämer M., “Sphärische Untergruppen in kompacten zusammenhängenden Liegruppen”, Compositio Math., 38 (1979), 129–153 | MR | Zbl

[16] Brion M., “Classification des espaces homogènes sphériques”, Compositio Math., 63 (1987), 189–208 | MR | Zbl

[17] Panyushev D. I., “Complexity of quasiaffine homogeneous varieties, $t$-decompositions, and affine homogeneous spaces of complexity 1”, Adv. Soviet Math., 8 (1992), 151–166 | MR | Zbl

[18] Elashvili A. G., “Kanonicheskii vid i statsionarnye podalgebry tochek obschego polozheniya dlya prostykh lineinykh grupp Li”, Funkts. analiz i ego prilozh., 6:1 (1972), 51–62 | MR | Zbl

[19] Panyushev D. I., “Complexity and rank of homogeneous spaces”, Geom. Dedicata, 34 (1990), 249–269 | DOI | MR | Zbl

[20] Panyushev D. I., “Complexity and nilpotent orbits”, Manuscripta Math., 83 (1994), 223–237 | DOI | MR | Zbl

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