Coefficients of normal Hilbert polynomials

DOI10.1016/S0021-8693(05)80052-3zbMath0756.13008MaRDI QIDQ1194196

Shiroh Itoh

Publication date: 27 September 1992

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

multiplicityCohen-Macaulay local ringlengthintegral closureHilbert polynomialsRees 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)

Related Items (26)

Tangent cones at curve and surface singularities ⋮ NORMAL HILBERT COEFFICIENTS AND ELLIPTIC IDEALS IN NORMAL TWO-DIMENSIONAL SINGULARITIES ⋮ Ratliff-Rush filtration, regularity and depth of higher associated graded modules. I ⋮ On the nonnegativity of normal Hilbert coefficients of two ideals ⋮ On the depth of the fiber cone of filtrations ⋮ Specialization and integral closure ⋮ Ratliff-Rush filtration, Hilbert coefficients and reduction number of integrally closed ideals ⋮ On the structure of the Sally module and the second normal Hilbert coefficient ⋮ Variations on the Grothendieck–Serre Formula for Hilbert Functions and Their Applications ⋮ RELATIVE HILBERT CO-EFFICIENTS ⋮ Postulation number of good filtrations ⋮ A filtration of the Sally module and the first normal Hilbert coefficient ⋮ Bounding the first Hilbert coefficient ⋮ NORMAL HILBERT FUNCTIONS OF ONE-DIMENSIONAL LOCAL RINGS ⋮ Bockstein cohomology of associated graded rings ⋮ Integral closure and generic elements ⋮ Results on the Hilbert coefficients and reduction numbers ⋮ Bounds on the normal Hilbert coefficients ⋮ On the Vanishing of the normal Hilbert coefficients of ideals ⋮ Tight closure of powers of ideals and tight hilbert polynomials ⋮ Minkowski inequality and equality for multiplicity of ideals of finite length in Noetherian local rings ⋮ Unnamed Item ⋮ Local cohomology of multi-Rees algebras with applications to joint reductions and complete ideals ⋮ Rees algebras and $p_g$-ideals in a two-dimensional normal local domain ⋮ On conjectures of Itoh and of Lipman on the cohomology of normalized blow-ups ⋮ Depth of associated graded rings via Hilbert coefficients of ideals

Cites Work

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• Genera and arithmetic genera of commutative rings
• Castelnuovo's regularity of graded rings and modules
• Hilbert functions and symbolic powers
• \(\Delta\)-genera and sectional genera of commutative rings
• Integral closures of ideals generated by regular sequences
• Pseudo-rational local rings and a theorem of Briancon-Skoda about integral closures of ideals
• On graded rings. I
• Die Sätze von Bertini für lokale Ringe
• A Note on Analytically Unramified Local Rings

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