Affine and unirational unique factorization domains with unmixed gradings

Source abstract

This paper studies the class of unique factorization domains B over an algebraically closed field k that are affine or unirational over k and that admit an effective unmixed Zd−1-grading with B0=k, where d is the dimension of B. Geometrically, these correspond to factorial affine k-varieties with an unmixed torus action of complexity one and trivial invariants. Our main result shows that this class is identical to the class of rings defined by trinomial data, thus generalizing earlier work of Mori, Ishida, and Hausen, Herppich, and Süss.