On the Makar-Limanov, Derksen invariants, and finite automorphism groups of algebraic varieties

TL;DR

This paper introduces new methods for constructing algebraic varieties with trivial Makar-Limanov invariants, computes Derksen invariants, and explores automorphism groups' properties, including their Jordan property.

Contribution

It presents a simple construction method for varieties with trivial Makar-Limanov invariants, generalizes invariants, and investigates automorphism groups' structure.

Findings

Constructed numerous varieties with trivial Makar-Limanov invariant

Computed Derksen invariants for specific varieties

Established results on the Jordan property of automorphism groups

Abstract

A simple method of constructing a big stock of algebraic varieties with trivial Makar-Limanov invariant is described, the Derksen invariant of some varieties is computed, the generalizations of the Makar-Limanov and Derksen invariants are introduced and discussed, and some results on the Jordan property of automorphism groups of algebraic varieties are obtained.