A counterexample to the fourteenth problem of Hilbert in dimension four (Q1887580)

From the author's abstract: This paper presents a family of new counterexamples to Hilbert's fourteenth problem. They are realized as subfields of the rational function field of four variables over a field of characteristic zero of transcendence degree three. It was previously not known whether any counterexample could be found as a subfield of a rational function field of four variables, or whether counterexamples with minimal transcendence degree three could exist.