Related papers: Infinite transitivity on affine varieties
In this paper we prove criteria for a nonnormal toric variety to be flexible, to be rigid and to be almost rigid. For rigid and almost rigid toric varieties we describe the automorphism group explicitly.
We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.
We present sufficient conditions for the triviality of the automorphism group of regular Toeplitz subshifts and give a broad class of examples from the class of $\mathcal{B}$-free subshifts satisfying them, extending [10]. On the other hand…
In this note, we extend the inductions and restrictions of modules over finite groups to non-injective group homomorphisms, establishing transitivity, Frobenius reciprocity, Mackey's formula, etc.
We study transitivity properties of graphs with more than one end. We completely classify the distance-transitive such graphs and, for all $k \geq 3$, the $k$-CS-transitive such graphs.
This is a survey article on moduli of affine schemes equipped with an action of a reductive group. The emphasis is on examples and applications to the classification of spherical varieties.
In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by…
We prove that a quasi-finite endomorphism of an algebraic variety over an algebraically closed field of characteristic zero, that is injective on the complement of a closed subvariety, is an automorphism. We also prove that an endomorphism…
We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.
We outline a new approach to classify real forms and automorphisms of finite order of affine Kac-Moody algebras.
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…
We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.
In this work we obtain sufficient conditions for a variety with a torus action of complexity one to have a finite number of automorphism group orbits.
The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K. Vogtmann's work, have been written about a lot. In…
We consider the totally nonfree (TNF) action of a groups and the corresponding adjoint invariant (AD) measures on the lattices of the subgroups of the given group. The main result is the description of all adjoint-invariant and TNF-measures…
We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…
We study analogues of Tate's conjecture on homomorphisms for abelian varieties when the ground field is finitely generated over an algebraic closure of a finite field. Our results cover the case of abelian varieties without nontrivial…
We study finite dimensional representations of the quantum affine algebra, using geometry of quiver varieties introduced by the author. As an application, we obtain character formulas expressed in terms of intersection cohomologies of…
We study automorphisms of the affine line over rings like ZZ/p^n.
Conditions are given under which an infinitesimal automorphism of a torsion-free connection preserving a symplectic form is necessarily a symplectic vector field. An example is given of a compact symplectic manifold admitting a flat…