Lower bound on Hilbert-Kunz multiplicities and maximal F-signatures
Lower bound on Hilbert-Kunz multiplicities and maximal F-signatures
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Hilbert-Kunz 重数和最大 F 签名的下界
DOI：
10.1017/s0305004122000238
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Ken-ichi Yoshida
中科院分区：
文献类型：
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作者：
Jack Jefferies; Yusuke Nakajima;Ilya Smirnov,Kei-ichi Watanabe;Ken-ichi Yoshida
希尔伯特-昆兹重数和F-签名是具有正特征的交换环的数值不变量，用来衡量奇点的严重程度：对于正则环，这两个不变量都等于一，在温和的假设下，反之亦然。一个自然的问题是，对于哪些奇异环，这些不变量最接近于一个。对于希尔伯特-昆兹重数，这个问题最早是由最后两位作者考虑的，并引起了极大的关注。在这篇文章中，我们研究了F-签名的一个上界问题，并重新讨论了Hilbert-kunz重数的下界。
Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and the converse holds under mild assumptions. A natural question is for what singular rings these invariants are closest to one. For Hilbert–Kunz multiplicity this question was first considered by the last two authors and attracted significant attention. In this paper, we study this question, i.e., an upper bound, for F-signature and revisit lower bounds on Hilbert–Kunz multiplicity.