Tight closure of powers of ideals and tight hilbert polynomials

DOI10.1017/S0305004119000215zbMath1478.13008arXiv1806.07522MaRDI QIDQ4958664

Vivek Mukundan, Kriti Goel, Jugal Kishore Verma

Publication date: 14 September 2021

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.07522

zbMATH Keywords

admissible filtrationtight Hilbert polynomialnormal Hilbert coefficientsF-rational rings

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items (5)

Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex ⋮ Tight Hilbert polynomial and F-rational local rings ⋮ Hilbert-Kunz function and Hilbert-Kunz multiplicity of some ideals of the Rees algebra ⋮ Tight closure of powers of parameter ideals in hypersurface rings and their tight Hilbert polynomials ⋮ Eakin-Sathaye-type theorems for joint reductions and good filtrations of ideals

Cites Work

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• Local cohomology of multi-Rees algebras with applications to joint reductions and complete ideals
• Integral closures of ideals generated by regular sequences
• Coefficients of normal Hilbert polynomials
• Bounds on the normal Hilbert coefficients
• Specialization and integral closure
• Hilbert Functions and Pseudo-Rational Local Rings of Dimension Two
• Form rings and regular sequences
• Hilbert Coefficients and the Depths of Associated Graded Rings
• A 𝑑-dimensional extension of a lemma of Huneke’s and formulas for the Hilbert coefficients
• A Note on Analytically Unramified Local Rings

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