A finite separating set for Daigle and Freudenburg's counterexample to Hilbert's Fourteenth Problem

TL;DR

This paper provides the first explicit example of a finite separating set within an invariant ring that is not finitely generated, specifically addressing Daigle and Freudenburg's 5-dimensional counterexample to Hilbert's Fourteenth Problem.

Contribution

It presents the first explicit finite separating set for a non-finitely generated invariant ring related to a notable counterexample.

Findings

Explicit finite separating set constructed for Daigle and Freudenburg's counterexample

Demonstrates existence of finite separating sets in non-finitely generated invariant rings

Advances understanding of invariant theory and Hilbert's Fourteenth Problem

Abstract

This paper gives the first explicit example of a finite separating set in an invariant ring which is not finitely generated, namely, for Daigle and Freudenburg's 5-dimensional counterexample to Hilbert's Fourteenth Problem.