Variation of Hilbert Coefficients

2012/03/26 by Laura Ghezzi, Shirô Gotô, Ghezzi, L. +5 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1203.5578

openalex publication_date 2012/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a Noetherian local ring (\RR, \m), the first two Hilbert coefficients, e₀ and e₁, of the I-adic filtration of an \m-primary ideal I are known to code for properties of \RR, of the blowup of \spec(\RR) along V(I), and even of their normalizations. We give estimations for these coefficients when I is enlarged (in the case of e₁ in the same integral closure class) for general Noetherian local rings.

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