The Picard Group of a G-Variety

@inproceedings{Knop1989ThePG,
  title={The Picard Group of a G-Variety},
  author={Friedrich Knop and Hanspeter Kraft and Thierry Vust},
  year={1989}
}
Let G be a reductive algebraic group and X an algebraic G-variety which admits a quotient it: X → X//G. In this article we describe several results concerning the Picard group Pic(X//G) of the quotient and the group Picc(X) of G-line bundles on X. For some further development of the subject we refer to the survey articles [Kr89a], [Kr89b]. 
Local Properties of Algebraic Group Actions
In this article we present a fundamental result due to Sumihiro. It states that every normal G-variety X, where G is a connected linear algebraic group, is locally isomorphic to a quasi-projective
Extended Picard complexes and linear algebraic groups
Abstract For a smooth geometrically integral variety X over a field k of characteristic 0, we introduce and investigate the extended Picard complex UPic(X). It is a certain complex of Galois modules
The cone of effective one—cycles of certain G —varieties
Let X be a normal projective variety admitting an action of a semisimple group with a unique closed orbit. We construct finitely many rational curves in X, all having a common point, such that every
Cartier divisors and geometry of normalG-varieties
We study Cartier divisors on normal varieties with the action of a reductive groupG. We give criteria for a divisor to be Cartier, globally generated and ample, and apply them to a study of the local
Homogeneous toric varieties
A description of transitive actions of a semisimple algebraic group G on toric varieties is obtained. Every toric variety admitting such an action lies between a product of punctured affine spaces
Homogeneous algebraic varieties and transitivity degree
. Let X be an algebraic variety such that the group Aut( X ) acts on X transitively. We define the transitivity degree of X as a maximal number m such that the action of Aut( X ) on X is m
Geometric Invariant Theory for principal three-dimensional subgroups acting on flag varieties
Let G be a semisimple complex Lie group. In this article, we study Geometric Invariant Theory on a flag variety G/B with respect to the action of a principal 3-dimensional simple subgroup S ⊂ G. We
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 20 REFERENCES
Local Properties of Algebraic Group Actions
In this article we present a fundamental result due to Sumihiro. It states that every normal G-variety X, where G is a connected linear algebraic group, is locally isomorphic to a quasi-projective
PICARD GROUPS OF HOMOGENEOUS SPACES OF LINEAR ALGEBRAIC GROUPS AND ONE-DIMENSIONAL HOMOGENEOUS VECTOR BUNDLES
We construct models of finite-dimensional linear and projective irreducible representations of a connected semisimple group G in linear systems on the variety G. We establish an algebro-geometric
Toroidal algebraic groups
Many of the more striking elementary properties of abelian varieties generalize to other kinds of algebraic groups, e.g. tori, i.e. direct products of multiplicative groups Gm, and in fact to
Algebraic Automorphisms of Affine Space
The following article is an updated version of the report [Kr85]; for convenience of the reader we have incorporated most of the material of that paper. Some other aspects can be found in the article
Geometric Invariant Theory
“Geometric Invariant Theory” by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to
Linear Algebraic Groups
Conventions and notation background material from algebraic geometry general notions associated with algebraic groups homogeneous spaces solvable groups Borel subgroups reductive groups rationality
Espaces fibrés algébriques
© Association des collaborateurs de Nicolas Bourbaki, 1954, tous droits réservés. L’accès aux archives du séminaire Bourbaki (http://www.bourbaki. ens.fr/) implique l’accord avec les conditions
Geometrische Methoden in der Invariantentheorie
Die vorliegende Einftihrung in die Invariantentheorie entstand aus einer Vorlesung, welche ich im Wintersemester 1977/78 in Bonn gehalten habe.Wie schon der Titel ausdruckt stehen dabei die
A lgebraic automorphisms of affine space In: Topological meth ods in algebraic transformation groups
  • Progress in Math
  • 1989
...
1
2
...