Abstract:We show that the subgraph of the concave transform of a multiplicative filtration on a section ring is the Newton–Okounkov body of a certain semigroup, and if the filtration is induced by a divisorial valuation, then the associated graded algebra is the algebra of sections of a concrete line bundle in higher dimension. We use this description to give a rationality criterion for certain Seshadri constants.

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中文翻译：

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过滤的凹变换和 Seshadri 常数的合理性

摘要：我们证明了截面环上乘法滤波的凹变换的子图是某个半群的 Newton-Okounkov 体，如果滤波是由一个除数求值引起的，那么相关的分级代数是高维混凝土线束的截面。我们使用这种描述来给出某些 Seshadri 常数的合理性标准。

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