Displaying similar documents to “Introduction to actions of algebraic groups”

Quotients of toric varieties by actions of subtori

Joanna Święcicka (1999)

Colloquium Mathematicae

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Let X be an algebraic toric variety with respect to an action of an algebraic torus S. Let Σ be the corresponding fan. The aim of this paper is to investigate open subsets of X with a good quotient by the (induced) action of a subtorus T ⊂ S. It turns out that it is enough to consider open S-invariant subsets of X with a good quotient by T. These subsets can be described by subfans of Σ. We give a description of such subfans and also a description of fans corresponding to quotient varieties....

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.

Equivariant degenerations of spherical modules for groups of type A

Stavros Argyrios Papadakis, Bart Van Steirteghem (2012)

Annales de l’institut Fourier

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V. Alexeev and M. Brion introduced, for a given a complex reductive group, a moduli scheme of affine spherical varieties with prescribed weight monoid. We provide new examples of this moduli scheme by proving that it is an affine space when the given group is of type A and the prescribed weight monoid is that of a spherical module.

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 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.