Lectures on spherical and wonderful varieties
نویسندگان
چکیده
منابع مشابه
Automorphisms of Wonderful Varieties
Let G be a complex semisimple linear algebraic group, and X a wonderful G-variety. We determine the connected automorphism group Aut(X) and we calculate Luna’s invariants of X under its action.
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1 Four constructions 1 1.1 First construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Second construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Third construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Fourth construction . . . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملWonderful Varieties of Type E
The classification of spherical varieties is already known for semisimple groups of types A and D. Adding type E, we complete the classification for all semisimple groups with a simply laced Dynkin diagram.
متن کاملSimple Immersions of Wonderful Varieties
Let G be a semisimple connected linear algebraic group over C, and X a wonderful G-variety. We study the possibility of realizing X as a closed subvariety of the projective space of a simple G-module. For any wonderful variety X we give a necessary and sufficient condition in terms of its set of spherical roots, which are certain characters of B (a fixed Borel subgroup of G) associated to the G...
متن کاملClassification of Strict Wonderful Varieties
In the setting of strict wonderful varieties we answer positively to Luna’s conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that strict wonderful varieties are mostly obtained from symmetric spaces, spherical nilpotent orbits or model spaces. To make the paper self-contained as much as possible, we sha...
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ژورنال
عنوان ژورنال: Les cours du CIRM
سال: 2010
ISSN: 2108-7164
DOI: 10.5802/ccirm.3