Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Regeta, Andriy"'
Let X be an irreducible variety and Bir(X) its group of birational transformations. We show that the group structure of Bir(X) determines whether X is rational and whether X is ruled. Additionally, we prove that any Borel subgroup of Bir(X) has deriv
Externí odkaz:
http://arxiv.org/abs/2409.07864
We give a description of the algebraic families of birational transformations of an algebraic variety X. As an application, we show that the morphisms to Bir(X) given by algebraic families satisfy a Chevalley type result and a certain fibre-dimension
Externí odkaz:
http://arxiv.org/abs/2409.06475
A monomial algebra B is defined as a quotient of a polynomial ring by a monomial ideal, which is an ideal generated by a finite set of monomials. In this paper, we determine the automorphism group of a monomial algebra B, under the assumption that B
Externí odkaz:
http://arxiv.org/abs/2408.02197
The length of an element $z$ of a Lie algebra $L$ is defined as the smallest number $s$ needed to represent $z$ as a sum of $s$ brackets. The bracket width of $L$ is defined as supremum of the lengths of its elements. Given a finite-dimensional simpl
Externí odkaz:
http://arxiv.org/abs/2404.06045
In this paper we show that a normal affine toric variety X different from the algebraic torus is uniquely determined by its automorphism group in the category of affine irreducible, not necessarily normal, algebraic varieties if and only if X is isom
Externí odkaz:
http://arxiv.org/abs/2308.08040
Autor:
Makedonskyi, Ievgen, Regeta, Andriy
We prove that the bracket width of the simple Lie algebra of vector fields $\rm{Vec}(C)$ of a smooth irreducible affine curve $C$ with a trivial tangent sheaf is at most three. In addition, if $C$ is a plane curve, the bracket width of $\rm{Vec}(C)$
Externí odkaz:
http://arxiv.org/abs/2210.14787
Autor:
Regeta, Andriy
Let $Aut_{alg}(X)$ be the subgroup of the group of regular automorphisms $Aut(X)$ of an affine algebraic variety $X$ generated by all connected algebraic subgroups. We prove that if $dim X \ge 2$ and if $Aut_{alg}(X)$ is rich enough, $Aut_{alg}(X)$ i
Externí odkaz:
http://arxiv.org/abs/2205.14653
Autor:
Perepechko, Alexander, Regeta, Andriy
Given an affine algebraic variety $X$, we prove that if the neutral component $\mathrm{Aut}^\circ(X)$ of the automorphism group consists of algebraic elements, then it is nested, i.e., is a direct limit of algebraic subgroups. This improves our earli
Externí odkaz:
http://arxiv.org/abs/2203.08950
Autor:
Regeta, Andriy
In this note we prove that if $S$ is an affine non-toric $\mathbb{G}_m$-surface of hyperbolic type that admits a $\mathbb{G}_a$-action and $X$ is an affine irreducible variety such that $Aut(X)$ is isomorphic to $Aut(S)$ as an abstract group, then $X
Externí odkaz:
http://arxiv.org/abs/2202.10761