Related papers: Equivariant birational geometry of linear actions

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.

The study of $G$-equivariant operators is of great interest to explain and understand the architecture of neural networks. In this paper we show that each linear $G$-equivariant operator can be produced by a suitable permutant measure,…

We study quotients of projective and affine spaces by various actions of the icosahedral group. Basically we concentrate on the rationality questions.

We study the equivariant cobordism theory of schemes for action of linear algebraic groups. We compare the equivariant cobordism theory for the action of a linear algebraic groups with similar groups for the action of tori and deduce some…

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.

Two fundamental ways to represent a group are as permutations and as matrices. In this paper, we study linear representations of groups that intertwine with a permutation representation. Recently, D'Alconzo and Di Scala investigated how…

We introduce an equivariant version of Hochschild cohomology as the deformation cohomology to study equivariant deformations of associative algebras equipped with finite group actions.

We investigate linearity of amalgams of subgroups of algebraic groups along intersections with algebraic subgroups. In the process, we establish linearity of certain "doubles" of linear groups, and obtain new examples of finitely generated…

In this paper, we first discuss cohomology and a one-parameter formal deformation theory of Lie-Yamaguti algebras. Next, we study finite group actions on Lie-Yamaguti algebras and introduce equivariant cohomology for Lie-Yamaguti algebras…

In this article we discuss some general results on the covariant Picard groupoid in the context of differential geometry and interpret the problem of lifting Lie algebra actions to line bundles in the Picard groupoid approach.

We study actions of finite groups on moduli spaces of stable holomorphic vector bundles and relate the fixed-point sets of those actions to representation varieties of certain orbifold fundamental groups.

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…

Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to…

We introduce and study functorial and combinatorial constructions concerning equivariant Burnside groups.

Dendriform algebras are certain associative algebras whose product splits into two binary operations and the associativity splits into three new identities. In this paper, we study finite group actions on dendriform algebras. We define…

We discuss the notion of essential dimension of a finite group and explain its relation with birational algebraic geometry. We show how this leads to a (partial) classification of simple finite groups of essential dimension less than or…

We investigate the birational geometry of Deligne-Mumford stacks and define new birational invariants in this context.

We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.

In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weak Factorization Theorems of nonsingular projective…