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arXiv · 1308.2917

Hilbert regularity of ZZ-graded modules over polynomial rings

Winfried Bruns·Julio José Moyano-Fernández·Jan Uliczka
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Abstract

Let M be a finitely generated ZZ-graded module over the standard graded polynomial ring R=K[X_1, ..., X_n] 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.

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Winfried Bruns, Julio José Moyano-Fernández, Jan Uliczka. 2013-08-13. Hilbert regularity of ZZ-graded modules over polynomial rings. https://arxiv.org/abs/1308.2917

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