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Les cours du CIRM

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Paolo Bravi
Classification of spherical varieties
Les cours du CIRM, 1 no. 1: Hamiltonian Actions: invariants et classification (2010), p. 99-111, doi: 10.5802/ccirm.5
Article PDF | 2 citations in Cedram

Résumé - Abstract

We give a short introduction to the problem of classification of spherical varieties, by presenting the Luna conjecture about the classification of wonderful varieties and illustrating some of the related currently known results.

Bibliography

[A] D.N. Ahiezer, Equivariant completions of homogeneous algebraic varieties by homogeneous divisors, Ann. Global Anal. Geom. 1 (1983), 49–78.  MR 739893 |  Zbl 0537.14033
[AB] V. Alexeev, M. Brion, Moduli of affine schemes with reductive group action, J. Algebraic Geom. 14 (2005), 83–117.  MR 2092127 |  Zbl 1081.14005
[Bra] P. Bravi, Wonderful varieties of type $E$, Represent. Theory, 11 (2007), 174–191.  MR 2346359 |  Zbl 1135.14037
[BC08] P. Bravi, S. Cupit-Foutou, Equivariant deformations of the affine multicone over a flag variety, Adv. Math. 217 (2008), 2800–2821.  MR 2397467 |  Zbl 1171.14029
[BC10] P. Bravi, S. Cupit-Foutou, Classification of strict wonderful varieties, Ann. Inst. Fourier (Grenoble) 60 (2010), to appear.
[BL09] P. Bravi, D. Luna, An introduction to wonderful varieties with many examples of type F4, J. Algebra, to appear.
[BP05] P. Bravi, G. Pezzini, Wonderful varieties of type $D$, Represent. Theory, 9 (2005), 578–637.  MR 2183057 |  Zbl pre05241714
[BP09] P. Bravi, G. Pezzini, Wonderful varieties of type B and C, arXiv:0909.3771v1 .
[Bri87] M. Brion, Classification des espaces homogènes sphériques, Compositio Math. 63 (1987), 189–208. Numdam |  MR 906369 |  Zbl 0642.14011
[Bri90] M. Brion, Vers une généralisation des espaces symétriques, J. Algebra 134 (1990), 115–143.  MR 1068418 |  Zbl 0729.14038
[Bri] M. Brion, in this volume. Cedram
[C08] S. Cupit-Foutou, Invariant Hilbert schemes and wonderful varieties, arXiv:0811.1567v2 . arXiv
[C09] S. Cupit-Foutou, Wonderful varieties: a geometrical realization, arXiv:0907.2852v1 . arXiv
[DGMP] C. De Concini, M. Goresky, R. MacPharson, C. Procesi, On the geometry of quadrics and their degenerations, Comment. Math. Helv. 63 (1988), 337–413.  MR 960767 |  Zbl 0693.14023
[DP] C. De Concini, C. Procesi, Complete symmetric varieties, Invariant theory (Montecatini, 1982), Lecture Notes in Math. 996, 1–44, Springer, Berlin, 1983.  MR 718125 |  Zbl 0581.14041
[HS] M. Haiman, B. Sturmfels, Multigraded Hilbert schemes, J. Algebraic Geom. 13 (2004), 725–769.  MR 2073194 |  Zbl 1072.14007
[Kn] F. Knop, Automorphisms, root systems, and compactifications of homogeneous varieties, J. Amer. Math. Soc. 9 (1996), 153–174.  MR 1311823 |  Zbl 0862.14034
[Kr] M. Krämer, Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen, Compositio Math. 38 (1979), 129–153. Numdam |  MR 528837 |  Zbl 0402.22006
[Lo09] I.V. Losev, Uniqueness property for spherical homogeneous spaces, Duke Math. J. 147 No. 2 (2009), 315–343. Article |  MR 2495078 |  Zbl 1175.14035
[Lo10] I.V. Losev, Proof of the Knop conjecture, Ann. Inst. Fourier (Grenoble), 59 (2009), no. 3, 1105–1134. Cedram |  MR 2543664 |  Zbl pre05580736
[Lo] I.V. Losev, in this volume. Cedram
[Lu96] D. Luna, Toute variété magnifique est sphérique, Transform. Groups 1 (1996), 249–258.  MR 1417712 |  Zbl 0912.14017
[Lu01] D. Luna, Variétés sphériques de type $A$, Publ. Math. Inst. Hautes Études Sci. 94 (2001), 161–226. Numdam |  MR 1896179 |  Zbl 1085.14039
[LV] D. Luna, T. Vust, Plongements d’espaces homogènes, Comment. Math. Helv. 58 (1983), no. 2, 186–245.  MR 705534 |  Zbl 0545.14010
[Mi] I.V. Mikityuk, On the integrability of invariant hamiltonian systems with homogeneous configurations spaces (in Russian), Math. Sbornik 129, 171 (1986), 514–534.  MR 842398 |  Zbl 0621.70005
[P07] G. Pezzini, Simple immersions of wonderful varieties, Math. Z. 255 (2007), 793–812.  MR 2274535 |  Zbl 1122.14036
[P] G. Pezzini, in this volume. Cedram
[W] B. Wasserman, Wonderful varieties of rank two, Transform. Groups 1 (1996), 375–403.  MR 1424449 |  Zbl 0921.14031
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