A numerical characterization of the \(S_{2}\)-ification of a Rees algebra

DOI10.1016/S0022-4049(02)00157-3zbMath1088.13501arXivmath/0209293MaRDI QIDQ1861493

Cătălin Ciupercă

Publication date: 9 March 2003

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0209293

zbMATH Keywords

first coefficient idealgeneralization of the Hilbert coefficientsSerre \((S_2)\)-property

Mathematics Subject Classification ID

Multiplicity theory and related topics (13H15) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (18)

On the first generalized Hilbert coefficient and depth of associated graded rings ⋮ Generalized Hilbert coefficients and Northcott's inequality ⋮ Different approaches of coefficient ideals ⋮ A generalization of coefficient ideals ⋮ Multiplicities for arbitrary modules and reduction ⋮ The core of zero-dimensional monomial ideals ⋮ Generalized Samuel Multiplicities of Monomial Ideals and Volumes ⋮ Some properties of the multiplicity sequence for arbitrary ideals ⋮ Hilbert functions of multigraded algebras, mixed multiplicities of ideals and their applications ⋮ Hilbert polynomials of j-transforms ⋮ Multiplicity sequence and integral dependence ⋮ Mixed multiplicities, Segre numbers and Segre classes ⋮ Generalized Hilbert Functions ⋮ Reduction numbers of equimultiple ideals ⋮ Degrees of multiplicity functions for equimultiple ideals ⋮ Equimultiple coefficient modules ⋮ The Cohen–Macaulay and Gorenstein Properties of Rings Associated to Filtrations ⋮ Asymptotic behavior of lengths of coefficient ideals

Uses Software

• Macaulay2

Cites Work

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• Some basic results on canonical modules
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• Multiplicity for ideals of maximal analytic spread and intersection theory
• Multiplicities of a bigraded ring and intersection theory
• Einige Bemerkungen zur Theorie der ganz-algebraischen Abhängigkeit von Idealen
• First coefficient domains and ideals of reduction number one
• Coefficient Ideals
• Joins and Intersections
• First coefficient ideals and the \(S_2\)-ification of a Rees algebra
• A numerical characterization of reduction ideals

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