khovanski -有限值，有理曲线和环面作用

Pub Date : 2018-07-23 DOI:10.4171/jca/41

N. Ilten, Milena Wrobel

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引用次数: 9

摘要

我们研究（多）分次域上的全秩齐次估值，并询问它们何时具有有限的Khovanskii基。我们证明了从多分级域到简单分级域的自然减少。作为特例，我们考虑有理曲线的投影坐标环，以及几乎复曲面的变体。我们的结果涉及Kaveh和Manon提出的几个问题，并暗示Bossinger Lamboglia Mincheva Mohammadi生产热带原锥的程序一般不会终止。

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Khovanskii-finite valuations, rational curves, and torus actions

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.

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