The cylinder over the Koras-Russell cubic threefold has a trivial Makar-Limanov invariant

TL;DR

This paper proves that the cylinder over the Koras-Russell cubic threefold has a trivial Makar-Limanov invariant, indicating the absence of non-constant invariant regular functions under additive group actions.

Contribution

It establishes the triviality of the Makar-Limanov invariant for the cylinder over the Koras-Russell cubic threefold, a significant result in affine algebraic geometry.

Findings

The Makar-Limanov invariant of the cylinder over the Koras-Russell cubic is trivial.

Regular functions invariant under additive group actions are constants.

Supports the understanding of automorphism groups of affine threefolds.

Abstract

We show that the Makar-Limanov invariant of the cylinder over the Koras-Russell cubic affine threefold is trivial. This means that regular functions which are invariant under all algebraic actions of the additive group on this variety are constants.