All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 23

Showing per page

Oka manifolds: From Oka to Stein and back

Franc Forstnerič (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations...

On complete orbit spaces of SL(2) actions, II

Andrzej Białynicki-Birula, Joanna Święcicka (1992)

Colloquium Mathematicae

The aim of this paper is to extend the results of [BB-Ś2] concerning geometric quotients of actions of SL(2) to the case of good quotients. Thus the results of the present paper can be applied to any action of SL(2) on a complete smooth algebraic variety, while the theorems proved in [BB-Ś2] concerned only special situations.

On deformation method in invariant theory

Dmitri Panyushev (1997)

Annales de l'institut Fourier

In this paper we relate the deformation method in invariant theory to spherical subgroups. Let G be a reductive group, Z an affine G -variety and H ⊂ G a spherical subgroup. We show that whenever G / H is affine and its semigroup of weights is saturated, the algebra of H -invariant regular functions on Z has a G -invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of G . The deformation method in its usual form, as developed...

On existence of double coset varieties

Artem Anisimov (2012)

Colloquium Mathematicae

Let G be a complex affine algebraic group and H,F ⊂ G be closed subgroups. The homogeneous space G/H can be equipped with the structure of a smooth quasiprojective variety. The situation is different for double coset varieties F∖∖G//H. We give examples showing that the variety F∖∖G//H does not necessarily exist. We also address the question of existence of F∖∖G//H in the category of constructible spaces and show that under sufficiently general assumptions F∖∖G//H does exist as a constructible space....

On quasihomogeneous manifolds – via Brion-Luna-Vust theorem

Marco Andreatta, Jarosław A. Wiśniewski (2003)

Bollettino dell'Unione Matematica Italiana

We consider a smooth projective variety X on which a simple algebraic group G acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of G with the induced action of G on the normal bundle of a closed orbit of the action. We get effective results in case G = S ⁢ L ⁢ n and dim ⁡ X ≤ 2 ⁢ n - 2 .

On spherical nilpotent orbits and beyond

Dmitri I. Panyushev (1999)

Annales de l'institut Fourier

We continue investigations that are concerned with the complexity of nilpotent orbits in semisimple Lie algebras. We give a characterization of the spherical nilpotent orbits in terms of minimal Levi subalgebras intersecting them. This provides a kind of canonical form for such orbits. A description minimal non-spherical orbits in all simple Lie algebras is obtained. The theory developed for the adjoint representation is then extended to Vinberg’s θ -groups. This yields a description of spherical...

On symmetric semialgebraic sets and orbit spaces

Ludwig Bröcker (1998)

Banach Center Publications

For a symmetric (= invariant under the action of a compact Lie group G) semialgebraic basic set C, described by s polynomial inequalities, we show, that C can also be written by s + 1 G-invariant polynomials. We also describe orbit spaces for the action of G by a number of inequalities only depending on the structure of G.

On the motive of a quotient variety.

Sebastián del Baño Rollin, Vicente Navarro Aznar (1998)

Collectanea Mathematica

We show that the motive of the quotient of a scheme by a finite group coincides with the invariant submotive.

Currently displaying 1 – 20 of 23

Page 1 Next