Lectures on spherical and wonderful varieties
Pezzini, Guido1
1 Departement Mathematik Universität Erlangen-Nürnberg Bismarckstraße 1 1 2 91054 Erlangen Deutschland
Actions hamiltoniennes : invariants et classification. 6 – 10 avril 2009, Les cours du CIRM, no. 1 (2010), pp. 33-53.

These notes contain an introduction to the theory of spherical and wonderful varieties. We describe the Luna-Vust theory of embeddings of spherical homogeneous spaces, and explain how wonderful varieties fit in the theory.

DOI : 10.5802/ccirm.3
Classification : 14J50, 14L30, 14M17
Pezzini, Guido 1

1 Departement Mathematik Universität Erlangen-Nürnberg Bismarckstraße 1 1 2 91054 Erlangen Deutschland 
@article{CCIRM_2010__1_1_33_0,
     author = {Pezzini, Guido},
     title = {Lectures on spherical and wonderful varieties},
     booktitle = {Actions hamiltoniennes~: invariants et classification. 6 {\textendash} 10 avril 2009},
     series = {Les cours du CIRM},
     pages = {33--53},
     publisher = {CIRM},
     number = {1},
     year = {2010},
     doi = {10.5802/ccirm.3},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/ccirm.3/}
}
TY  - JOUR
AU  - Pezzini, Guido
TI  - Lectures on spherical and wonderful varieties
BT  - Actions hamiltoniennes : invariants et classification. 6 – 10 avril 2009
AU  - Collectif
T3  - Les cours du CIRM
PY  - 2010
SP  - 33
EP  - 53
IS  - 1
PB  - CIRM
UR  - http://archive.numdam.org/articles/10.5802/ccirm.3/
DO  - 10.5802/ccirm.3
LA  - en
ID  - CCIRM_2010__1_1_33_0
ER  - 
%0 Journal Article
%A Pezzini, Guido
%T Lectures on spherical and wonderful varieties
%B Actions hamiltoniennes : invariants et classification. 6 – 10 avril 2009
%A Collectif
%S Les cours du CIRM
%D 2010
%P 33-53
%N 1
%I CIRM
%U http://archive.numdam.org/articles/10.5802/ccirm.3/
%R 10.5802/ccirm.3
%G en
%F CCIRM_2010__1_1_33_0
Pezzini, Guido. Lectures on spherical and wonderful varieties, dans Actions hamiltoniennes : invariants et classification. 6 – 10 avril 2009, Les cours du CIRM, no. 1 (2010), pp. 33-53. doi : 10.5802/ccirm.3. http://archive.numdam.org/articles/10.5802/ccirm.3/

[A83] D.N. Ahiezer, Equivariant completions of homogeneous algebraic varieties by homogeneous divisors, Ann. Global Anal. Geom. 1 (1983), no. 1, 49–78.

[B09] P. Bravi, Classification of spherical varieties, in this volume

[BL08] P. Bravi, D. Luna, An introduction to wonderful varieties with many examples of type F 4 , arXiv:0812.2340v1.

[Br89] M. Brion, On spherical varieties of rank one, CMS Conf. Proc. 10 (1989), 31–41.

[Br90] M. Brion, Vers une généralisation des espaces symétriques, J. Algebra 134 (1990), no. 1, 115–143.

[Br97] M. Brion, Variétés sphériques, http://www-fourier.ujf-grenoble.fr/∼mbrion/spheriques.ps

[Br09] M. Brion, Introduction to actions of algebraic groups, in this volume.

[DP83] C. De Concini, C. Procesi, Complete symmetric varieties, Invariant theory (Montecatini, 1982), Lecture Notes in Math., 996, Springer, Berlin, 1983, 1–44.

[F93] W. Fulton, Introduction to toric varieties, Ann. of Math. Stud. 131, Princeton University Press, Princeton, NJ, 1993.

[H75] J. Humphreys, Linear algebraic groups, Graduate Texts in Mathematics, 21, Springer-Verlag, New York-Heidelberg, 1975.

[HS82] A. Huckleberry, D. Snow, Almost-homogeneous Kähler manifolds with hypersurface orbits, Osaka J. of Math. 19 (1982), 763–786.

[K91] F. Knop., The Luna-Vust theory of spherical embeddings, Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), 225–249, Manoj Prakashan, Madras, 1991.

[K96] F. Knop, Automorphisms, root systems, and compactifications of homogeneous varieties, J. Amer. Math. Soc. 9 (1996), no. 1, 153–174.

[KKLV89] F. Knop, H. Kraft, D. Luna, T. Vust, Local properties of algebraic group actions, Algebraische Transformationsgruppen und Invariantentheorie (H. Kraft, P. Slodowy, T. Springer eds.) DMV-Seminar 13, Birkhäuser Verlag (Basel-Boston) (1989) 63–76.

[L07] I. Losev, Uniqueness property for spherical homogeneous spaces, Duke Mathematical Journal 147 (2009), no. 2, 315–343.

[Lu96] D. Luna, Toute variété magnifique est sphérique, Transform. Groups 1 (1996), no. 3, 249–258.

[Lu97] D. Luna, Grosses cellules pour les variétés sphériques, Algebraic groups and Lie groups, Austral. Math. Soc. Lect. Ser., 9, Cambridge Univ. Press, Cambridge, 1997, 267–280.

[Lu01] D. Luna, Variétés sphériques de type A, Inst. Hautes Études Sci. Publ. Math. 94 (2001), 161–226.

[LV83] Luna, D. and Vust, T., Plongements d’espaces homogènes, Comment. Math. Helv. 58 (1983), no. 2, 186–245.

[T06] D.A. Timashev, Homogeneous spaces and equivariant embedding, arXiv:math/0602228v1.

Cité par Sources :