Automorphisms of Danielewski varieties

TL;DR

This paper characterizes the automorphism groups of Danielewski varieties, extending previous results on Danielewski surfaces, and contributes to understanding their algebraic structure and symmetries.

Contribution

It generalizes the description of automorphisms from Danielewski surfaces to higher-dimensional Danielewski varieties.

Findings

Automorphism groups of Danielewski varieties are explicitly described.

The results extend known automorphism structures from surfaces to higher dimensions.

Provides insights into the algebraic symmetries of these varieties.

Abstract

In 2007, Dubouloz introduced Danielewski varieties. Such varieties generalize Danielewski surfaces and provide counterexamples to generalized Zariski cancellation problem in arbitrary dimension. In the present work we describe the automorphism group of a Danielewski variety. This result is a generalization of a description of automorphisms of Danielewski surfaces due to Makar-Limanov.