摘要翻译：
Mustata、Takagi和Watanabe在[F阈值和Bernstein-Sato多项式]中定义了F阈值，它是特征$P$环上理想对的不变量。本文证明了正则局部环上检验理想的F-阈值等于跳跃数。本文给出了环上F-阈值的一个公式。这个公式是[Huneke,Mustata,Takagi和Watanabe：F-阈值、紧闭包、整闭包和多重界]中例子的推广。我们证明了f-跳跃系数与f-阈值之间存在一个不等式。特别地，我们观察到F-纯阈值和F-阈值之间的比较。作为应用，我们证明了由单纯锥定义的多环正则性的刻划，以及F-阈值在某些情况下的合理性。
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英文标题：
《Formulas of F-thresholds and F-jumping coefficients on toric rings》
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作者：
Daisuke Hirose
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Commutative Algebra        交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  F-thresholds are defined by Mustata, Takagi and Watanabe in [F-thresholds and Bernstein-Sato polynomials], which are invariants of the pair of ideals on rings of characteristic $p$. In their paper, it is proved F-thresholds equal to jumping numbers for the test ideal on regular local rings. In this note, we give an formula of F-thresholds on toric rings. This formula is a generalization of the example in [Huneke, Mustata, Takagi and Watanabe:F-thresholds, tight closure, integral closure, and multiplicity bounds]. We prove that there exists an inequality between F-jumping coefficients and F-thresholds. In particular, we observe a comparison between F-pure thresholds and F-thresholds. As applications, we prove the characterization of regularity for toric rings defined by a simplicial cone, and the rationality of F-thresholds in some cases.
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PDF链接：
https://arxiv.org/pdf/0709.1627