ﻻ يوجد ملخص باللغة العربية
The main result asserts: Let $G$ be a reductive, affine algebraic group and let $(rho ,V)$ be a regular representation of $G$. Let $X$ be an irreducible $mathbb{C}^{ times } G$ invariant Zariski closed subset such that $G$ has a closed orbit that has maximal dimension among all orbits (this is equivalent to: generic orbits are closed). Then there exists an open subset, $W$,of $X$ in the metric topology which is dense with complement of measure $0$ such that if $x ,y in W$ then $left (mathbb{C}^{ times } Gright )_{x}$ is conjugate to $left (mathbb{C}^{ times } Gright )_{y}$. Furthermore, if $G x$ is a closed orbit of maximal dimension and if $x$ is a smooth point of $X$ then there exists $y in W$ such that $left (mathbb{C}^{ times } Gright )_{x}$ contains a conjugate of $left (mathbb{C}^{ times } Gright )_{y}$. The proof involves using the Kempf-Ness theorem to reduce the result to the principal orbit type theorem for compact Lie groups.
An textit{algebraic} action of a discrete group $Gamma $ is a homomorphism from $Gamma $ to the group of continuous automorphisms of a compact abelian group $X$. By duality, such an action of $Gamma $ is determined by a module $M=widehat{X}$ over the
In this article we review the question of constructing geometric quotients of actions of linear algebraic groups on irreducible varieties over algebraically closed fields of characteristic zero, in the spirit of Mumfords geometric invariant theory (G
In this paper, we show Langtons type theorem on separatedness and properness of moduli functor of torsion free semistable sheaves on algebraic orbifolds over an algebraically closed field k
We show that the principal algebraic actions of countably infinite groups associated to lopsided elements in the integral group ring satisfying some orderability condition are Bernoulli.
We establish the analogue of the Friedlander-Mazur conjecture for Tehs reduced Lawson homology groups of real varieties, which says that the reduced Lawson homology of a real quasi-projective variety $X$ vanishes in homological degrees larger than th