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Given an irreducible representation $V$ of a complex simply connected semisimple algebraic group $G$ we consider the closure $X$ of the image of $G$ in $ℙ (End (V))$ . We determine for which $V$ the variety $X$ is normal and for which $V$ is smooth.

On a separation of orbits in the module variety for domestic canonical algebras

Piotr Dowbor, Andrzej Mróz (2008)

Colloquium Mathematicae

Given a pair M,M' of finite-dimensional modules over a domestic canonical algebra Λ, we give a fully verifiable criterion, in terms of a finite set of simple linear algebra invariants, deciding if M and M' lie in the same orbit in the module variety, or equivalently, if M and M' are isomorphic.

On actions of $ℂ^{*}$ on algebraic spaces

Andrzej Bialynicki-Birula (1993)

Annales de l'institut Fourier

The main result of the paper says that all schematic points of the source of an action of $C^{*}$ on an algebraic space $X$ are schematic on $X$ .

On automorphisms of Enriques surfaces.

I. Dolgachev (1984)

Inventiones mathematicae

On Automorphisms of the Affine Cremona Group

Hanspeter Kraft, Immanuel Stampfli (2013)

Annales de l’institut Fourier

We show that every automorphism of the group $𝒢_{n} : = A u t (𝔸^{n})$ of polynomial automorphisms of complex affine $n$ -space $𝔸^{n} = ℂ^{n}$ is inner up to field automorphisms when restricted to the subgroup $T 𝒢_{n}$ of tame automorphisms. This generalizes a result of Julie Deserti who proved this in dimension $n = 2$ where all automorphisms are tame: $T 𝒢_{2} = 𝒢_{2}$ . The methods are different, based on arguments from algebraic group actions.

On complete orbit spaces of SL(2) actions

Andrzej Białynicki-Birula, Joanna Święcicka (1988)

Colloquium Mathematicae

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 complex affine surfaces with ...-action.

Karl-Heinz Fieseler (1994)

Commentarii mathematici Helvetici

On conjugating representations and adjoint representations of semisimple groups.

S. Donkin (1988)

Inventiones mathematicae

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 $H \subset G$ 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 Drinfeld's universal formal group over the p-adic upper half plane.

Jeremy Teitelbaum (1989)

Mathematische Annalen

On Exact Actions of Unipotent Groups.

Masanori Koitabashi (1995)

Manuscripta mathematica

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 functional equations of complex powers.

J.-L Igusa (1986)

Inventiones mathematicae

On hypersurface quotient singularities of dimension 4.

Chiang, Li, Roan, Shi-Shyr (2004)

International Journal of Mathematics and Mathematical Sciences

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