In the setting of strict wonderful varieties we prove Luna’s conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that primitive strict wonderful varieties are mostly obtained from symmetric spaces, spherical nilpotent orbits and model spaces. To make the paper as self-contained as possible, we also gather some known results on these families and more generally on wonderful varieties.
D’après la conjecture de Luna, les variétés magnifiques peuvent être classifiées en termes d’objets combinatoires, les systèmes sphériques. Dans le présent article, nous prouvons cette conjecture dans le cas des variétés magnifiques dites strictes. Nous montrons, en particulier, que les variétés magnifiques strictes et primitives sont, pour la plupart, des variétés symétriques, des orbites nilpotentes sphériques ou des espaces modèles. Afin de faciliter la lecture de cet article, nous rappelons quelques faits connus sur ces variétés et, plus généralement, sur les variétés magnifiques.
Keywords: Spherical varieties, wonderful varieties, symmetric varieties, spherical nilpotent orbits, model spaces
Mot clés : variétés sphériques, variétés magnifiques, variétés symétriques, orbites nilpotentes sphériques, espaces modèles
@article{AIF_2010__60_2_641_0, author = {Bravi, Paolo and Cupit-Foutou, St\'ephanie}, title = {Classification of strict wonderful varieties}, journal = {Annales de l'Institut Fourier}, pages = {641--681}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {2}, year = {2010}, doi = {10.5802/aif.2535}, zbl = {1195.14068}, mrnumber = {2667789}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2535/} }
TY - JOUR AU - Bravi, Paolo AU - Cupit-Foutou, Stéphanie TI - Classification of strict wonderful varieties JO - Annales de l'Institut Fourier PY - 2010 SP - 641 EP - 681 VL - 60 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2535/ DO - 10.5802/aif.2535 LA - en ID - AIF_2010__60_2_641_0 ER -
%0 Journal Article %A Bravi, Paolo %A Cupit-Foutou, Stéphanie %T Classification of strict wonderful varieties %J Annales de l'Institut Fourier %D 2010 %P 641-681 %V 60 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2535/ %R 10.5802/aif.2535 %G en %F AIF_2010__60_2_641_0
Bravi, Paolo; Cupit-Foutou, Stéphanie. Classification of strict wonderful varieties. Annales de l'Institut Fourier, Volume 60 (2010) no. 2, pp. 641-681. doi : 10.5802/aif.2535. http://archive.numdam.org/articles/10.5802/aif.2535/
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