The finite generation ideal for Daigle & Freudenberg's counterexample to Hilbert's fourteenth problem

Abstract

We compute the finite generation ideal for Daigle and Freudenburg's counterexample to Hilbert's fourteenth problem. This ideal helps to understand how far the ring of invariants is from being finitely generated. Our calculations show that the finite generation ideal is the radical of an ideal generated by three infinite families of invariants. We show that these three families together with an additional invariant form a SAGBI-basis. We use the properties of our SAGBI-basis in our computation of the finite generation ideal.