Core and residual intersections of ideals

DOI10.1090/S0002-9947-02-02908-2zbMath1013.13001arXivmath/0210070MaRDI QIDQ2782654

Claudia Polini, Alberto Corso, Bernd Ulrich

Publication date: 8 April 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210070

zbMATH Keywords

reductionscore of an idealintegral closureresidual intersections of ideals

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Linkage, complete intersections and determinantal ideals (13C40) Integral closure of commutative rings and ideals (13B22) Ideals and multiplicative ideal theory in commutative rings (13A15) Local cohomology and commutative rings (13D45) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (24)

Minimal reductions and core of ideals in pullbacks ⋮ The core of ideals in arbitrary characteristic ⋮ Good ideals and \(p_g\)-ideals in two-dimensional normal singularities ⋮ Core versus graded core, and global sections of line bundles ⋮ The core of zero-dimensional monomial ideals ⋮ Core of ideals in one-dimensional Noetherian domains ⋮ Core of ideals in integral domains ⋮ Coefficient ideals in dimension two ⋮ Minimal reductions and cores of edge ideals ⋮ Residual intersections and core of modules ⋮ Reductions and Core of Ideals in Integral Domains: Some Recent Developments ⋮ A characterization of two-dimensional rational singularities via core of ideals ⋮ BLOWUPS AND FIBERS OF MORPHISMS ⋮ Computing the core of ideals in arbitrary characteristic ⋮ A Short Note on Containment of Cores ⋮ Artin-Nagata properties, minimal multiplicities, and depth of fiber cones ⋮ The cl-core of an ideal ⋮ A formula for the core of an ideal ⋮ Core of ideals of Noetherian local rings ⋮ Symmetry in the core of a zero-dimensional monomial ideal ⋮ Bound on the Multiplicity of Almost Complete Intersections ⋮ A formula for the *-core of an ideal ⋮ Nakayama closures, interior operations, and core-hull duality -- with applications to tight closure theory ⋮ Integral closure, basically full closure, and duals of nonresidual closure operations

Uses Software

• Macaulay2

Cites Work

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• The Koszul algebra of a codimension 2 embedding
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• What annihilates a module?
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• Coefficient ideals and the Cohen-Macaulay property of Rees algebras
• On residually $S_2$ ideals and projective dimension one modules
• Self-linked curve singularities
• Form rings and regular sequences
• Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers
• Linkage and the Koszul Homology of Ideals
• A theorem of Briançon-Skoda type for regular local rings containing a field
• Ideals Having the Expected Reduction Number
• Ideals with sliding depth
• Residual intersections in Cohen-Macaulay rings
• Fiber cones and the integral closure of ideals
• The structure of the core of ideals

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