Asymptotic linear bounds for the Castelnuovo-Mumford regularity

DOI10.1090/S0002-9947-02-02932-XzbMath1012.13006arXivmath/0101086OpenAlexW1810384317MaRDI QIDQ2781384

Jürgen Herzog, Lê Tuân Hoa, Ngô Viêt Trung

Publication date: 19 March 2002

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

Full work available at URL: https://arxiv.org/abs/math/0101086

zbMATH Keywords

associated graded ringCastelnuovo-Mumford regularityinitial idealreduction number\(a\)-invariantfiltrations of homogeneous ideals

Mathematics Subject Classification ID

Local cohomology and commutative rings (13D45) Local cohomology and algebraic geometry (14B15) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Real algebraic and real-analytic geometry (14P99)

Related Items

Asymptotic behavior of integer programming and the stability of the Castelnuovo-Mumford regularity ⋮ Survey on Regularity of Symbolic Powers of an Edge Ideal ⋮ Asymptotic behavior of reduction numbers ⋮ Castelnuovo-Mumford regularity of initial ideals ⋮ Symbolic powers of monomial ideals and vertex cover algebras ⋮ Comparison between regularity of small symbolic powers and ordinary powers of an edge ideal ⋮ Regularity of symbolic powers and arboricity of matroids ⋮ Asymptotic invariants constructed from generic initial ideals ⋮ A computation of the Castelnuovo-Mumford regularity of certain two-dimensional unmixed ideals ⋮ Binomial expansion for saturated and symbolic powers of sums of ideals ⋮ Frobenius methods in combinatorics ⋮ Mixed multiplicities of graded families of ideals ⋮ Partial Castelnuovo–Mumford regularities of sums and intersections of powers of monomial ideals ⋮ Non-linear behaviour of Castelnuovo-Mumford regularity ⋮ Castelnuovo–Mumford Regularity of Sums of Powers of Polynomial Ideals ⋮ Regularity and Koszul property of symbolic powers of monomial ideals ⋮ Symbolic powers of certain cover ideals of graphs ⋮ Asymptotic Hilbert polynomials and limiting shapes ⋮ Castelnuovo-Mumford regularity of symbolic powers of two-dimensional square-free monomial ideals

Cites Work

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• Asymptotic prime divisors
• Linear free resolutions and minimal multiplicity
• On graded rings. I
• On the Castelnuovo-Mumford regularity and the arithmetic degree of monomial ideals
• Graded Betti numbers of some embedded rational \(n\)-folds
• Powers of ideals. Primary decompositions, Artin-Rees lemma and regularity
• Four counterexamples in combinatorial algebraic geometry
• Comparison of symbolic and ordinary powers of ideals.
• Reduction Exponent and Degree Bound for the Defining Equations of Graded Rings
• Vanishing Theorems, A Theorem of Severi, and the Equations Defining Projective Varieties
• Form rings and regular sequences
• A Sharp Bound for the Regularity Index of Fat Points in General Position
• The Castelnuovo regularity of the Rees algebra and the associated graded ring
• Linear Bounds on Growth of Associated Primes
• Regularity of the powers of an ideal
• Irrational asymptotic behaviour of Castelnuovo-Mumford regularity
• Gröbner bases, local cohomology and reduction number
• Asymptotic behaviour of Castelnuovo-Mumford regularity
• On multigraded resolutions
• Uniform bounds and symbolic powers on smooth varieties
• Positivity and complexity of ideal sheaves