A. Regeta

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math.AG2026

The bracket width for Lie algebras of vector fields is finite

Rafael B. Andrist, Andriy Regeta

We prove that the bracket width of the Lie algebra of vector fields on any smooth affine algebraic variety of dimension $n$ is at most $(n + 1)^{2}$ . We give improved bounds for some f…

math.AG2026

Solvable Automorphism Groups of Varieties

Serge Cantat, Hanspeter Kraft, Andriy Regeta +1

Let $X$ be a variety of dimension $n$ , and let $Aut (X)$ be its automorphism group. When $X$ is quasi-affine, we prove that a solvable subgroup of $Aut (X)$ that is…

math.AG2026

On Ramanujam's Theorem About Finite Dimensional Groups of Automorphisms

Serge Cantat, Hanspeter Kraft, Andriy Regeta +1

Ramanujam's theorem states that any connected finite-dimensional subgroup of the automorphism group $Aut (X)$ of an irreducible variety $X$ is an algebraic group, in a natu…

math.AG2026

The Automorphism groups of zero-dimensional monomial algebras

Roberto DÃaz, Alvaro Liendo, Gonzalo Manzano-Flores +1

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 au…

math.AG2025

Characterizing Varieties Using Birational Transformations

Nathan Chen, Louis Esser, Andriy Regeta +2

Suppose $X$ is an irreducible complex variety. We show that when $X$ is ruled, the group of birational transformations $B i r (X)$ , as a group, determines $X$ up to birational transfo…

math.AG2024

Group Theoretical Characterizations of Rationality

Andriy Regeta, Christian Urech, Immanuel van Santen

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 rul…