The Automorphism Group of Certain Factorial Threefolds and a Cancellation Problem

TL;DR

This paper determines the automorphism groups of specific factorial complex affine threefolds with additive group actions and presents new counterexamples to a generalized cancellation problem.

Contribution

It explicitly computes automorphism groups for certain threefolds and introduces novel counterexamples to the cancellation problem.

Findings

Automorphism groups are explicitly determined.

New counterexamples to the generalized cancellation problem are provided.

Advances understanding of affine threefolds with additive group actions.

Abstract

The automorphism groups of certain factorial complex affine threefolds admitting locally trivial actions of the additive group are determined. As a consequence new counterexamples to a generalized cancellation problem are obtained.