Hilbert-Kunz Multiplicity of Three-Dimensional Local Rings

DOI10.1017/S0027763000009053zbMath1076.13009arXivmath/0307294OpenAlexW2950492784MaRDI QIDQ4676028

Ken-ichi Yoshida, Kei- ichi Watanabe

Publication date: 6 May 2005

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0307294

zbMATH Keywords

tight closureHilbert-Kunz multiplicitythree-dimensional complete local ring

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Multiplicity theory and related topics (13H15) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Regular local rings (13H05)

Related Items (15)

Bounds on the Hilbert-Kunz multiplicity ⋮ Fundamental groups of $F$-regular singularities via $F$-signature ⋮ Hilbert-Kunz density function and asymptotic Hilbert-Kunz multiplicity for projective toric varieties ⋮ Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension ⋮ $F$-singularities: applications of characteristic $p$ methods to singularity theory ⋮ On lower bounds for \(s\)-multiplicities ⋮ The Hilbert-Kunz density functions of quadric hypersurfaces ⋮ \(F\)-signature exists ⋮ Computing the invariants of intersection algebras of principal monomial ideals ⋮ On the upper semi-continuity of the Hilbert-Kunz multiplicity ⋮ The shape of Hilbert-Kunz functions ⋮ Asymptotic Lech's inequality ⋮ New estimates of Hilbert–Kunz multiplicities for local rings of fixed dimension ⋮ Lower bounds on Hilbert–Kunz multiplicities and maximal F-signatures ⋮ The rationality of the Hilbert-Kunz multiplicity in graded dimension two

Cites Work

• Some surprising Hilbert-Kunz functions
• Hilbert-Kunz functions of cubic curves and surfaces
• Hilbert-Kunz multiplicity and an inequality between multiplicity and colength
• Hilbert-Kunz function of monomial ideals and binomial hypersurfaces
• The Hilbert-Kunz function
• Hilbert--Kunz functions and multiplicities for full flag varieties and elliptic curves.
• Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings
• Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular
• Notes on Hilbert-Kunz Multiplicity of Rees Algebras
• BOUNDS ON MULTIPLICITIES OF LOCAL RINGS
• On rings with small Hilbert-Kunz multiplicity
• Hilbert-Kunz multiplicity, McKay correspondence and good ideals in two-dimensional rational singularities
• Multiplicity and tight closures of parameters

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