MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Khovanskii-Finite Valuations, Rational Curves, and Torus Actions

Nathan Ilten and Milena Wrobel


We study full rank homogeneous valuations on (multi)-graded domains and ask when they have finite Khovanskii bases. We show that there is a natural reduction from multigraded to simply graded domains. As special cases, we consider projective coordinate rings of rational curves, and almost toric varieties. Our results relate to several problems posed by Kaveh and Manon, and imply that the procedure of Bossinger-Lamboglia-Mincheva-Mohammadi for producing tropical prime cones will not terminate in general.

Aug 2, 2018
Aug 10, 2018

Related publications

2020 Repository Open Access
Nathan Ilten and Milena Wrobel

Khovanskii-Finite valuations, rational curves, and torus actions

In: Journal of combinatorial algebra, 4 (2020) 2, pp. 141-166