2024-03-29T11:02:13Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1682872022-11-08T08:27:16Zcom_10234_7037com_10234_9col_10234_8635
Repositori UJI
author
Bruns, Winfried
author
Moyano-Fernández, Julio José
author
Uliczka, Jan
2017-07-13T09:28:59Z
2017-07-13T09:28:59Z
2017-06
BRUNS, Winfried; MOYANO-FERNÁNDEZ, Julio José; ULICZKA, Jan. Hilbert regularity of Z-graded modules over polynomial rings. Journal of Commutative Algebra 9, no. 2, 2017, pp. 157-184.
http://hdl.handle.net/10234/168287
http://dx.doi.org/10.1216/JCA-2017-9-2-157
Let M be a finitely generated Z-graded module over the standard graded polynomial ring R=K[X1,…,Xd] with K a field, and let HM(t)=QM(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 HM. 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 QM(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.
eng
Hilbert regularity
boundary presentation of a rational function
nonnegative power series
Hilbert depth
Hilbert regularity of Z-graded modules over polynomial rings
info:eu-repo/semantics/article
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bruns_2017.pdf.txt