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Graded algebras with cyclotomic Hilbert series
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Borzì, Alessio and D'Alì, Alessio (2021) Graded algebras with cyclotomic Hilbert series. Journal of Pure and Applied Algebra, 225 (12). 106764. doi:10.1016/j.jpaa.2021.106764 ISSN 0022-4049.
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Official URL: https://doi.org/10.1016/j.jpaa.2021.106764
Abstract
Let R be a positively graded algebra over a field k. We say that R is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all of its roots on the unit circle. Such rings arise naturally in commutative algebra, numerical semigroup theory and Ehrhart theory. If R is standard graded, we prove that, under the additional hypothesis that R is Koszul or has an irreducible h-polynomial, Hilbert-cyclotomic algebras coincide with complete intersections. In the Koszul case, this is a consequence of some classical results about the vanishing of deviations of a graded algebra.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
SWORD Depositor: | Library Publications Router | ||||||||
Journal or Publication Title: | Journal of Pure and Applied Algebra | ||||||||
Publisher: | Elsevier | ||||||||
ISSN: | 0022-4049 | ||||||||
Official Date: | December 2021 | ||||||||
Dates: |
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Volume: | 225 | ||||||||
Number: | 12 | ||||||||
Article Number: | 106764 | ||||||||
DOI: | 10.1016/j.jpaa.2021.106764 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Open Access Version: |
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