F-purity of hypersurfaces
F-purity of hypersurfaces
复制标题
超曲面的 F 纯度
DOI：
10.4310/mrl.2012.v19.n2.a11
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
D. Hern'andez
中科院分区：
文献类型：
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作者：
D. Hern'andez
在这篇注记中，我们研究了对的F-纯性，并证明了(与对数正则情形一样)F-纯性保持在F-纯门限处。我们还刻画了当F-纯度等价于尖锐F-纯度时，这是[Sch08]中引入的关于配对的另一种纯洁性概念。这些关于门槛纯度的结果推广了[Har06，Sch08]中的结果，预计该领域的许多专家都会持有这些结果。最后，我们将[BMS09]中关于所有F-纯阈值集合的结果推广到最一般的设置。
In this note, we study F-purity of pairs, and show (as is the case with log canonicity) that F-purity is preserved at the F-pure threshold. We also characterize when F-purity is equivalent to sharp F-purity, an alternate notion of purity for pairs introduced in [Sch08]. These results on purity at the threshold generalize results appearing in [Har06, Sch08], and were expected to hold by many experts in the field. We conclude by extending results in [BMS09] on the set of all F-pure thresholds to the most general setting.