Infinite transitivity on affine varieties

TL;DR

This paper surveys recent advances in automorphism groups of affine algebraic varieties, focusing on infinite transitivity, flexibility, and their geometric implications, while highlighting constructions, examples, and open problems.

Contribution

It provides a comprehensive overview of recent results on infinite transitivity and flexibility in affine varieties, including new constructions and open questions.

Findings

Automorphism groups can act infinitely transitively on affine varieties.

Flexibility of affine varieties is closely related to their automorphism groups.

The paper discusses applications and open problems in the field.

Abstract

In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.