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

DOI10.1017/S0305004122000238MaRDI QIDQ5877288

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

Publication date: 10 February 2023

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.06166

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Singularities in algebraic geometry (14B05) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items

The Hilbert-Kunz density functions of quadric hypersurfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Maximal modifications and Auslander-Reiten duality for non-isolated singularities
• Separating invariants and local cohomology
• \(F\)-signature exists
• Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension
• \(F\)-regular and \(F\)-pure normal graded rings
• Some surprising Hilbert-Kunz functions
• Notes on the Hilbert-Kunz function.
• Minimal relative Hilbert-Kunz multiplicity
• The \(F\)-signature and strong \(F\)-regularity.
• Hilbert-Kunz multiplicity and an inequality between multiplicity and colength
• \(F\)-signature and Hilbert-Kunz multiplicity: a combined approach and comparison
• On the upper semi-continuity of the Hilbert-Kunz multiplicity
• The F-signature of an affine semigroup ring
• Divisorial linear algebra of normal semigroup rings
• The Hilbert-Kunz function
• Certain invariant subrings are Gorenstein. I
• Two theorems about maximal Cohen-Macaulay modules
• Generalized \(F\)-signatures of Hibi rings
• Equimultiplicity theory of strongly \(F\)-regular rings
• Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions
• Noncommutative resolution, F-blowups and \(D\)-modules
• Observations on the \(F\)-signature of local rings of characteristic \(p\)
• Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings
• New estimates of Hilbert–Kunz multiplicities for local rings of fixed dimension
• Valuations Associated with Ideals (II)
• Upper bound of multiplicity of F-pure rings
• Tight closure and strong F-regularity
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Polytopes, Rings, and K-Theory
• Maximally generated Cohen-Macaulay modules.
• On Noetherian Rings of Characteristic p
• F-Regularity, Test Elements, and Smooth Base Change
• Simplicity of Rings of Differential Operators in Prime Characteristic
• -SIGNATURE UNDER BIRATIONAL MORPHISMS
• Hilbert-Kunz Multiplicity of Three-Dimensional Local Rings
• On rings with small Hilbert-Kunz multiplicity
• Finite torsors over strongly $F$-regular singularities
• On Dual F-Signature
• Colength, multiplicity, and ideal closure operations
• Characterizations of Regular Local Rings of Characteristic p
• MODULES WITH FINITE $F$-REPRESENTATION TYPE
• Multiplicity and tight closures of parameters