Displaying similar documents to “Spherical roots of spherical varieties”

Spherical varieties and Wahl’s conjecture

Nicolas Perrin (2014)

Annales de l’institut Fourier

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Using the theory of spherical varieties, we give a type independent very short proof of Wahl’s conjecture for cominuscule homogeneous varieties for all primes different from 2.

Classification of spherical varieties

Paolo Bravi (2010)

Les cours du CIRM

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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.

Lectures on spherical and wonderful varieties

Guido Pezzini (2010)

Les cours du CIRM

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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.

Uniqueness properties for spherical varieties

Ivan Losev (2010)

Les cours du CIRM

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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...

Classification of strict wonderful varieties

Paolo Bravi, Stéphanie Cupit-Foutou (2010)

Annales de l’institut Fourier

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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.