Paolo Bravi (2010)
Les cours du CIRM
Similarity:
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.
Guido Pezzini (2010)
Les cours du CIRM
Similarity:
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.
Michel Brion (2010)
Les cours du CIRM
Similarity:
These notes present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures.
Paolo Bravi, Stéphanie Cupit-Foutou (2010)
Annales de l’institut Fourier
Similarity:
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.
Andrzej Daszkiewicz, Tomasz Przebinda (1996)
Colloquium Mathematicae
Similarity:
The purpose of this note is to show that the Orbit Conjecture of C. Benson, J. Jenkins, R. L. Lipsman and G. Ratcliff [BJLR1] is true. Another proof of that fact has been given by those authors in [BJLR2]. Their proof is based on their earlier results, announced together with the conjecture in [BJLR1]. We follow another path: using a geometric quantization result of Guillemin-Sternberg [G-S] we reduce the conjecture to a similar statement for a projective space, which is a special case...
Dmitri I. Panyushev (1995)
Annales de l'institut Fourier
Similarity:
We study -actions of the form , where is the dual (to ) -variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action is given. It is shown that the doubled actions have a number of nice properties, if is spherical or of complexity one.