Hilbert regularity of Z-graded modules over polynomial rings
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Other documents of the author: Bruns, Winfried; Moyano-Fernández, Julio José; Uliczka, Jan
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comunitat-uji-handle3:10234/8635
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Title
Hilbert regularity of Z-graded modules over polynomial ringsDate
2017-06Publisher
Rocky Mountain Mathematics ConsortiumBibliographic citation
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.Type
info:eu-repo/semantics/articlePublisher version
http://projecteuclid.org/euclid.jca/1496476820#abstractVersion
info:eu-repo/semantics/sumittedVersionSubject
Abstract
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 ... [+]
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. [-]
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Journal of Commutative Algebra 9, no. 2, 2017Rights
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info:eu-repo/semantics/openAccess
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