Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings

DOI10.1017/S0027763000007819zbMath1018.13008OpenAlexW1784375627MaRDI QIDQ2731032

Ken-ichi Yoshida, Kei- ichi Watanabe

Publication date: 14 September 2003

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

Full work available at URL: https://doi.org/10.1017/s0027763000007819

zbMATH Keywords

characteristic \(p\)Hilbert-Kunz multiplicityFrobenius powerlocal Noetherian ringstable idealsVeronese subrings

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Multiplicity theory and related topics (13H15) 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 (18)

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 ⋮ On rings with small Hilbert-Kunz multiplicity ⋮ $F$-singularities: applications of characteristic $p$ methods to singularity theory ⋮ Asymptotic Hilbert-Kunz multiplicity ⋮ On lower bounds for \(s\)-multiplicities ⋮ Notes on the Hilbert-Kunz function. ⋮ On the Hilbert-Samuel coefficients of Frobenius powers of an ideal ⋮ Hilbert-Kunz multiplicity of products of ideals ⋮ Hilbert-Kunz Multiplicity of Three-Dimensional Local Rings ⋮ Notes on Hilbert-Kunz Multiplicity of Rees Algebras ⋮ Multiplicity and Hilbert-Kunz multiplicity of monoid rings. ⋮ Hilbert–Kunz multiplicity of the powers of an ideal ⋮ 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

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• The Hilbert-Kunz function
• On the coefficients of the Hilbert polynomial
• Rational singularities, with applications to algebraic surfaces and unique factorization
• Joint reductions of complete ideals
• Joint reductions and Rees algebras

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