The primary components of and integral closures of ideals in 3-dimensional regular local rings

DOI10.1007/BF01459141zbMath0605.13003MaRDI QIDQ1084137

Craig Huneke

Publication date: 1986

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164174

zbMATH Keywords

symbolic powers of ideals3-dimensional regular local ringintegral closures of ideals

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Ideals and multiplicative ideal theory in commutative rings (13A15) Regular local rings (13H05)

Related Items

Integral Closures of Cohen-Macaulay Monomial Ideals ⋮ Symbolic Rees Algebras ⋮ On the Cohen-Macaulayness of the conormal module of an ideal ⋮ A deformation theory for non-isolated singularities ⋮ Explicit computations on symbolic powers of monomial curves in affine space ⋮ Factorization of complete ideals ⋮ Birational extensions in dimension two and integrally closed ideals ⋮ Singular schemes of hypersurfaces ⋮ Remark on Rees valuations of finitely supported complete monomial ideals in a regular local ring ⋮ Finitely supported \(\ast\)-simple complete ideals and multiplicities in a regular local ring ⋮ On the relation type of large powers of an ideal ⋮ Self-linked curve singularities ⋮ Finitely supported \(\ast\)-simple complete ideals in a regular local ring ⋮ Prime ideals associated to symmetric powers of a module ⋮ Arithmetically cohen-macaulay monomial curves in ℙ³ ⋮ Weak subintegral closure of ideals ⋮ Integral closure and other operations on monomial ideals ⋮ Asymptotic prime divisors of torsion-free symmetric powers of modules ⋮ On the equality of ordinary and symbolic powers of ideals ⋮ Comparison of symbolic and ordinary powers of parity binomial edge ideals ⋮ Symbolic powers of codimension two Cohen-Macaulay ideals ⋮ Symbolic powers of prime ideals with applications to hypersurface rings ⋮ A stable version of Harbourne's conjecture and the containment problem for space monomial curves ⋮ Expected resurgences and symbolic powers of ideals ⋮ The symbolic defect of an ideal ⋮ Rees Algebras of Ideals Having Small Analytic Deviation ⋮ The Gorensteinness of the Symbolic Blow-Ups for Certain Space Monomial Curves ⋮ Joint reductions of complete ideals ⋮ Lefschetz extensions, tight closure and big Cohen-Macaulay algebras ⋮ Many associated primes of powers of primes ⋮ Reductions and special parts of closures ⋮ Integrally closed and componentwise linear ideals ⋮ Non-Cohen-Macaulay Symbolic Blow-ups for Space Monomial Curves ⋮ Quadratic transform of complete ideals in regular local rings ⋮ Integrally Closed Modules Over Two-Dimensional Regular Local Rings ⋮ Depths of multiplier ideals and integral closure ⋮ Symbolic blowup algebras and invariants of certain monomial curves in an affine space ⋮ Embeddings of certain graded rings into their canonical modules ⋮ Tensor-multinomial sums of ideals: Primary decompositions and persistence of associated primes ⋮ Zariski factorization theory for sheaves of ideals on arithmetic three-folds ⋮ Primary decomposition of powers of the prime ideal of a numerical semigroup ring ⋮ The Rees Valuations of Complete Ideals in a Regular Local Ring ⋮ Prime filtrations of the powers of an ideal ⋮ LOCAL COHOMOLOGY OF MULTI-REES ALGEBRAS, JOINT REDUCTION NUMBERS AND PRODUCT OF COMPLETE IDEALS ⋮ The tight integral closure of a set of ideals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic prime divisors
• On linear complete intersections
• Symbolic powers of monomial curves
• Resolutions of the exterior and symmetric powers of a module
• On the associated graded ring of an ideal
• On asymptotic prime divisors
• On the finite generation of symbolic blow-ups
• Liaison des variétés algébriques. I
• Rational singularities, with applications to algebraic surfaces and unique factorization
• Valuations Associated with Ideals (II)
• A Prime Ideal in a Polynomial Ring Whose Symbolic Blow-up is Not Noetherian
• The Syzygies of the Conormal Module
• Hilbert Functions and Pseudo-Rational Local Rings of Dimension Two
• Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
• Linkage and the Koszul Homology of Ideals