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2017 Hilbert regularity of $\mathbb Z$-graded modules over polynomial rings
Winfried Bruns, Julio José Moyano-Fernández, Jan Uliczka
J. Commut. Algebra 9(2): 157-184 (2017). DOI: 10.1216/JCA-2017-9-2-157

Abstract

Let $M$ be a finitely generated $\mathbb{Z} $-graded module over the standard graded polynomial ring $R=K[X_1, \ldots , X_d]$ with $K$ a field, and let $H_M(t)=Q_M(t)/ (1-t)^d$ be the Hilbert series of~$M$. We introduce the Hilbert regularity of~$M$ as the lowest possible value of the Castelnuovo-Mumford regularity for an $R$-module with Hilbert series $H_M$. Our main result is an arithmetical description of this invariant which connects the Hilbert regularity of~$M$ to the smallest~$k$ such that the power series $Q_M(1-t)/(1-t)^k$ has no negative coefficients. Finally, we give an algorithm for the computation of the Hilbert regularity and the Hilbert depth of an $R$-module.

Citation

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Winfried Bruns. Julio José Moyano-Fernández. Jan Uliczka. "Hilbert regularity of $\mathbb Z$-graded modules over polynomial rings." J. Commut. Algebra 9 (2) 157 - 184, 2017. https://doi.org/10.1216/JCA-2017-9-2-157

Information

Published: 2017
First available in Project Euclid: 3 June 2017

zbMATH: 1366.13010
MathSciNet: MR3659947
Digital Object Identifier: 10.1216/JCA-2017-9-2-157

Subjects:
Primary: 13D40
Secondary: 13D45

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.9 • No. 2 • 2017
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