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Uniqueness properties for spherical varieties

Ivan Losev (2010)

Les cours du CIRM

The goal of these lectures is to explain speaker’s results on uniqueness properties of spherical varieties. By a uniqueness property we mean the following. Consider some special class of spherical varieties. Define some combinatorial invariants for spherical varieties from this class. The problem is to determine whether this set of invariants specifies a spherical variety in this class uniquely (up to an isomorphism). We are interested in three classes: smooth affine varieties, general affine varieties,...

Universal transitivity of simple and 2-simple prehomogeneous vector spaces

T. Kimura, S. Kasai, H. Hosokawa (1988)

Annales de l'institut Fourier

We denote by k a field of characteristic zero satisfying H 1 ( k , Aut ( S L 2 ) ) 0 . Let G be a connected k -split linear algebraic group acting on X = Aff n rationally by ρ with a Zariski-dense G -orbit Y . A prehomogeneous vector space ( G , ρ ,X) is called “universally transitive” if the set of k -rational points Y ( k ) is a single ρ ( G ) ...

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