Khovanskii-Finite Valuations, Rational Curves, and Torus Actions
Algebraic Geometry
2020-01-24 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1807.08780,
title = {Khovanskii-Finite Valuations, Rational Curves, and Torus Actions},
author = {Nathan Ilten and Milena Wrobel},
journal= {arXiv preprint arXiv:1807.08780},
year = {2020}
}
Comments
19 pages; v2 minor revisions