A. Regeta

activity

20092024

most citedAutomorphism Groups of Danielewski Surfaces

2 citations · 3 across the 9 of their papers we have counts for

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8 papers · 1 filter

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…

math.AG2024

The Structure of Algebraic Families of Birational Transformations

Andriy Regeta, Christian Urech, Immanuel van Santen

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…

math.AG2022

When is the automorphism group of an affine variety linear?

Andriy Regeta

Let $A u t_{a l g} (X)$ be the subgroup of the group of regular automorphisms $A u t (X)$ of an affine algebraic variety $X$ generated by all connected algebraic subgroups. We prove that i…

math.AG2022

Characterization of affine $G_{m}$ -surfaces of hyperbolic type

Andriy Regeta

In this note we prove that if $S$ is an affine non-toric $G_{m}$ -surface of hyperbolic type that admits a $G_{a}$ -action and $X$ is an affine irreducible variety such…

math.AG2021

Bracket width of simple Lie algebras

Adrien Dubouloz, Boris Kunyavskii, Andriy Regeta

The notion of commutator width of a group, defined as the smallest number of commutators needed to represent each element of the derived group as their product, has been extensivel…

math.AG2020

Small G-varieties

Hanspeter Kraft, Andriy Regeta, Susanna Zimmermann

An affine varieties with an action of a semisimple group $G$ is called "small" if every non-trivial $G$ -orbit in $X$ is isomorphic to the orbit of a highest weight vector. Such a v…