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Smooth Projective Symmetric Varieties with Picard Number equal to one
TLDR
In this paper, the smooth projective symmetric G-varieties with Picard number one (and G semisimple) were classified and a criterion for the smoothness of simple symmetric symmetric varieties whose closed orbit is complete.Abstract:
We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple) Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete In particular we prove that, given a such variety X which is not exceptional, then X is smooth if and only if an appropriate toric variety contained in X is smoothread more
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On some smooth projective two-orbit varieties with Picard number 1
TL;DR: In this paper, all smooth projective horospherical varieties with Picard number 1 were characterized and the automorphism group of any such variety X acts with at most two orbits and this group still acts with only two orbits on X blown up at the closed orbit.
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Geometrical description of smooth projective symmetric varieties with Picard number one
TL;DR: In this paper, a geometrical description of smooth projective symmetric G-varieties with Picard number one and G semisimpleteness is given, and a G-equivariant embedding of the variety X in a homogeneous variety is described.
Journal ArticleDOI
Smooth projective symmetric varieties with picard number one
TL;DR: In this paper, the smooth projective symmetric G-varieties with Picard number one (and G semisimple) were classified and a criterion for the smoothness of simple (normal) symmetric varieties whose closed orbit is complete was proposed.
Journal ArticleDOI
Fano symmetric varieties with low rank
TL;DR: In this article, the G-varietes symetriques projectives localement factorielles (respective of lisse) avec rang 2 which sont de Fano.
References
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Book
Introduction to Lie Algebras and Representation Theory
TL;DR: In this paper, Semisimple Lie Algebras and root systems are used for representation theory, isomorphism and conjugacy theorem, and existence theorem for representation.
Book
Representation Theory: A First Course
TL;DR: This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras.