Vanishing and non-negativity of the first normal Hilbert coefficient

DOI10.1007/s40306-024-00548-2MaRDI QIDQ6650701

Pham Hung Quy, Linquan Ma

Publication date: 9 December 2024

Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)

zbMATH Keywords

regular local ringsnormal Hilbert polynomialbig Cohen-Macaulay algebrasnormal Hilbert coefficientstight Hilbert coefficients

Mathematics Subject Classification ID

Multiplicity theory and related topics (13H15) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40)

Cites Work

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• The Chern coefficients of local rings
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• Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras
• Specialization and integral closure
• Cohen-Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals
• Hilbert Coefficients and the Depths of Associated Graded Rings
• Tight closure of powers of ideals and tight hilbert polynomials
• The positivity of the first coefficients of normal Hilbert polynomials
• Weak functoriality of Cohen-Macaulay algebras
• Colength, multiplicity, and ideal closure operations
• Uniform annihilators of systems of parameters
• Uniform Lech’s inequality
• Tight Hilbert polynomial and F-rational local rings

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