MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.


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