Homological Invariants of Powers of an Ideal

DOI10.2307/2160118zbMath0780.13007OpenAlexW4248665282MaRDI QIDQ4201605

Vijay Kodiyalam

Publication date: 1 September 1993

Full work available at URL: https://doi.org/10.2307/2160118

zbMATH Keywords

TorHilbert polynomialanalytic spreadExtBetti numberminimal number of generatorsgraded moduleBass numberasymptotic homological invariants of ideals

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Syzygies, resolutions, complexes and commutative rings (13D02) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (29)

Rooted order on minimal generators of powers of some cover ideals ⋮ On the degree of Hilbert polynomials associated to the torsion functor ⋮ Morse resolutions of powers of square-free monomial ideals of projective dimension one ⋮ On the embedded primary components of ideals. II ⋮ Decompositions of Betti Diagrams of Powers of Monomial Ideals: A Stability Conjecture ⋮ Bass and Betti numbers of \(A/I^n\) ⋮ On the Betti polynomials of certain graded ideals ⋮ Powers of monomial ideals with characteristic-dependent Betti numbers ⋮ The Betti polynomials of powers of an ideal ⋮ Graded Betti numbers of powers of ideals ⋮ Index of reducibility of parameter ideals and Cohen-Macaulay rings ⋮ Hilbert coefficients of a Cohen-Macaulay module. ⋮ Bivariate Hilbert functions for the torsion functor. ⋮ Rigidity of Linear Strands and Generic Initial Ideals ⋮ Coherent functors and asymptotic stability ⋮ Powers of sums and their homological invariants ⋮ On the Chern number of an ideal ⋮ Hilbert-Samuel polynomials for the contravariant extension functor ⋮ On the Betti numbers and Rees algebras of ideals with linear powers ⋮ On the degree of the Kodiyalam polynomials of a graded ideal in the polynomial ring ⋮ Stabilization of Boij-Söderberg decompositions of ideal powers ⋮ On the degree of Hilbert polynomials of derived functors ⋮ Constructing big indecomposable modules ⋮ Graded Betti numbers of good filtrations ⋮ The number of generators of the powers of an ideal ⋮ Hilbert-Samuel functions of modules over Cohen-Macaulay rings ⋮ Open loci of graded modules ⋮ An interpretation of depth(G(I)) and e₁(I) via the Sally module ⋮ Poincaré series of multiplier and test ideals

Cites Work

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• On the symmetric and Rees algebra of an ideal generated by a d-sequence
• Small homomorphisms of local rings
• A proof of the existence of minimal R-algebra resolutions
• Ideals defined by matrices and a certain complex associated with them
• Poincare Series of Modules Over Local Rings
• The asymptotic nature of the analytic spread
• Grade Sensitivity and Generic Perfection

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