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Mathematics > Algebraic Geometry

arXiv:1807.08780 (math)
[Submitted on 23 Jul 2018 (v1), last revised 22 Jan 2020 (this version, v2)]

Title:Khovanskii-Finite Valuations, Rational Curves, and Torus Actions

Authors:Nathan Ilten, Milena Wrobel
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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.
Comments: 19 pages; v2 minor revisions
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1807.08780 [math.AG]
  (or arXiv:1807.08780v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.08780

Submission history

From: Nathan Ilten [view email]
[v1] Mon, 23 Jul 2018 18:39:16 UTC (22 KB)
[v2] Wed, 22 Jan 2020 20:31:20 UTC (23 KB)
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