On induced actions of algebraic groups
In this paper we study the existence problem for products in the categories of quasi-projective and algebraic varieties and also in the category of algebraic spaces.
On invariants of a set of matrices.
On normal representations of G-actions on projective varieties.
On orbits of the automorphism group on an affine toric variety
Let X be an affine toric variety. The total coordinates on X provide a canonical presentation of X as a quotient of a vector space by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.
On quasihomogeneous manifolds – via Brion-Luna-Vust theorem
We consider a smooth projective variety on which a simple algebraic group acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of with the induced action of on the normal bundle of a closed orbit of the action. We get effective results in case and .
On semi-invariants of tilted algebras of type Aₙ
We prove that for algebras obtained by tilts from the path algebras of equioriented Dynkin diagrams of type Aₙ, the rings of semi-invariants are polynomial.
On SL(2)-actions without 3-dimensional orbits
On some reductive group actions on affine space II.
On spherical nilpotent orbits and beyond
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 -groups. This yields a description of spherical...
On symmetric semialgebraic sets and orbit spaces
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 complicatedness of the pair (g,K).
On the Euler number of an orbifold.
On the geometry of conjugacy classes in classical groupes.
On the linearization of actions of linearly reductive groups.
On the Moment Map of a Multiplicity Free Action
The purpose of this note is to show that the Orbit Conjecture of C. Benson, J. Jenkins, R. L. Lipsman and G. Ratcliff [BJLR1] is true. Another proof of that fact has been given by those authors in [BJLR2]. Their proof is based on their earlier results, announced together with the conjecture in [BJLR1]. We follow another path: using a geometric quantization result of Guillemin-Sternberg [G-S] we reduce the conjecture to a similar statement for a projective space, which is a special case of a characterization...
On the motive of a quotient variety.
We show that the motive of the quotient of a scheme by a finite group coincides with the invariant submotive.
On the Periods of Enriques Surfaces. II.
On the reflection representation in Springer's theory.
On the stability of subgroup actions on certain quasihomogeneous -varieties.
On the stratification of the moduli space of Mumford curves