JournalsjcaVol. 4, No. 2pp. 141–166

Khovanskii-finite valuations, rational curves, and torus actions

  • Nathan Ilten

    Simon Fraser University, Burnaby, Canada
  • Milena Wrobel

    Simon Fraser University, Burnaby, Canada
Khovanskii-finite valuations, rational curves, and torus actions cover

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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.

Cite this article

Nathan Ilten, Milena Wrobel, Khovanskii-finite valuations, rational curves, and torus actions. J. Comb. Algebra 4 (2020), no. 2, pp. 141–166

DOI 10.4171/JCA/41