Castelnuovo-Mumford regularity of deficiency modules

2009/01/06 by Markus Brodmann, Brodmann, Markus, Maryam Jahangiri +3
Computer Science · Mathematics · #13D40 #13D45 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0901.0690

openalex publication_date 2009/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let d ∈ \N and let M be a finitely generated graded module of dimension ≤ d over a Noetherian homogeneous ring R with local Artinian base ring R₀. Let \beg(M), \gendeg(M) and \reg(M) respectively denote the beginning, the generating degree and the Castelnuovo-Mumford regularity of M. If i ∈ \N₀ and n ∈ Z, let dⁱ_M(n) denote the R₀-length of the n-th graded component of the i-th R₊-transform module Dⁱ_R+(M) of M and let Kⁱ(M) denote the i-th deficiency module of M. Our main result says, that \reg(Kⁱ(M)) is bounded in terms of \beg(M) and the "diagonal values" d^j_M(-j) with j = 0,..., d-1. As an application of this we get a number of further bounding results for \reg(Kⁱ(M)).

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