Complete symmetric varieties

Simple immersions of wonderful varieties

“…Rank 1 varieties with H = N G H. These cases are those that satisfy the condition (R) of the theorem, thus we must prove that F L is a closed immersion into P(V * L ). Those which are complete symmetric varieties can be omitted, since for them this fact is true (see [DP83]); they are: (1A, n > 2), (2), (4), (6A), (8B), (7C, n > 2), (8C), (1D), (6D), (6), (12) (again we use the labels and the ordering of [Wa96]). …”

“…Wonderful varieties are projective algebraic varieties (for us, over the field of complex numbers C) endowed with an action of a semisimple connected algebraic group G, having certain properties which have been inspired by the compactifications of symmetric homogeneous spaces given by De Concini and Procesi in [DP83]. Wonderful varieties turn out to have a significant role in the theory of spherical varieties, which are a class of G-varieties representing a common generalization of flag varieties and toric varieties.…”

Sur la structure locale des variétés sphériques

“…Notre principale motivation pour trouver l'énoncé ci-dessus a été l'article [7] de C. DE CONCINI-T. A. SPRINGER, article dans lequel sont étudiées les décompositions cellulaires (à la BIALYNICKI-BIRULA, voir [2]) de certaines compactifications des espaces symétriques adjoints {voir aussi [6]). Dans la deuxième partie de notre travail, nous expliquons comment on peut adapter, grâce à ce qui précède, quelques-uns de leurs énoncés au cadre plus général des variétés sphériques.…”

Classification of strict wonderful varieties

“…The set of non-degenerate quadrics is isomorphic to the symmetric space P SL n+1 /P SO n+1 . Generalisations of the variety of complete quadrics were constructed and studied by De Concini and Procesi in [10] as they considered more general symmetric spaces.…”