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arXiv · 2002.06166

Lower bounds on Hilbert--Kunz multiplicities and maximal F-signatures

Jack Jeffries·Yusuke Nakajima·Ilya Smirnov·Kei-ichi Watanabe·Ken-ichi Yoshida
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Abstract

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.

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Jack Jeffries, Yusuke Nakajima, Ilya Smirnov, Kei-ichi Watanabe, Ken-ichi Yoshida. 2020-02-14. Lower bounds on Hilbert--Kunz multiplicities and maximal F-signatures. https://arxiv.org/abs/2002.06166

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