论文标题
希尔伯特（Hilbert）的下限 - 昆兹（Kunz）多重性和最大F-签名
Lower bounds on Hilbert--Kunz multiplicities and maximal F-signatures
论文作者
论文摘要
希尔伯特·昆兹（Hilbert-Kunz）的多重性和F-签名是衡量奇异性严重程度的正常特征的交换环的数值不变性：对于常规环而言，两个不变性都等于一个，并且在轻度假设下的匡威保持。一个自然的问题是，这些不变的奇数最接近一个。对于希尔伯特 - 昆兹的多重性而言，这个问题首先被最近的两位作者考虑，并引起了极大的关注。在本文中，我们研究了这个问题，即，上限，用于f-signature and to for Hilbert-kunz多重性。
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.
