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

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...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 2023-03, Vol.174 (2), p.247-271
Hauptverfasser: JEFFRIES, JACK, NAKAJIMA, YUSUKE, SMIRNOV, ILYA, WATANABE, KEI–ICHI, YOSHIDA, KEN–ICHI
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Sprache:eng
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Zusammenfassung: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004122000238