Difference of Hilbert series of homogeneous monoid algebras and their normalizations

Higashitani, Akihiro

doi:https://doi.org/10.1007/s00233-024-10414-0

Difference of Hilbert series of homogeneous monoid algebras and their normalizations

Higashitani, Akihiro

Semigroup Forum, 2024, 108(1), 101-114

Number of Access:213（2025-10-23 12:06 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/95020

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Title	Difference of Hilbert series of homogeneous monoid algebras and their normalizations
Creator	NRID 1000060723385 1000060723385 researchmap permalink 7000011220 7000011220 Scopus Author ID 36105210100 36105210100 ORCID 0000-0002-3824-425X 0000-0002-3824-425X CreatorName Higashitani, Akihiro
Subject	Affine monoid algebras
	Edge rings
	Hilbert series
	Serre’s condition (S2)
Description	The version of record of this article, first published in Semigroup Forum, is available online at Publisher’s website: https://doi.org/10.1007/s00233-024-10414-0.
Abstract	Let Q be an affine monoid, k[Q] the associated monoid k-algebra, and k[Q¯] its normalization, where we let k be a field. We discuss a difference of the Hilbert series of k[Q] and k[Q¯] in the case where k[Q] is homogeneous (i.e., standard graded). More precisely, we prove that if k[Q] satisfies Serre’s condition (S₂), then the degree of the h-polynomial of k[Q] is always greater than or equal to that of k[Q¯]. Moreover, we also show counterexamples of this statement if we drop the assumption (S₂).
Publisher	Springer
Source Title	Semigroup Forum
Volume (Issue)	108(1)
Page	101-114
Date of Issued	2024-03-11
Language	English
Handle URL	https://hdl.handle.net/11094/95020
PISSN	00371912
eISSN	14322137
Relation.isIdenticalTo	DOI (Publisher Version) https://doi.org/10.1007/s00233-024-10414-0
Access Rights	open access
CopyRight	This article is licensed under a Creative Commons Attribution 4.0 International License.
oaire:version	Version of Record
Category	学術雑誌論文 Journal Article

Resource Type	journal article
Local Type	Journal Article
DCMI Type	Text
DCTERMS.bibliographicCitation	Semigroup Forum. 2024, 108(1), p. 101-114
DC.title	Difference of Hilbert series of homogeneous monoid algebras and their normalizations
DC.creator	Higashitani, Akihiro
DC.publisher	Springer
DC.language' scheme='DCTERMS.RFC1766	English
DC.type' scheme='DCTERMS.DCMIType	Text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2024-03-11
DC.identifier	https://doi.org/10.1007/s00233-024-10414-0
DC.subject	Affine monoid algebras
	Edge rings
	Hilbert series
	Serre’s condition (S2)
DC.description	The version of record of this article, first published in Semigroup Forum, is available online at Publisher’s website: https://doi.org/10.1007/s00233-024-10414-0.
DCTERMS.abstract	Let Q be an affine monoid, k[Q] the associated monoid k-algebra, and k[Q¯] its normalization, where we let k be a field. We discuss a difference of the Hilbert series of k[Q] and k[Q¯] in the case where k[Q] is homogeneous (i.e., standard graded). More precisely, we prove that if k[Q] satisfies Serre’s condition (S₂), then the degree of the h-polynomial of k[Q] is always greater than or equal to that of k[Q¯]. Moreover, we also show counterexamples of this statement if we drop the assumption (S₂).
DC.rights	This article is licensed under a Creative Commons Attribution 4.0 International License.
DC.format	95020
citation_title	Difference of Hilbert series of homogeneous monoid algebras and their normalizations
citation_author	Higashitani, Akihiro
citation_publisher	Springer
citation_language	English
citation_date	2024-03-11
citation_journal_title	Semigroup Forum
citation_volume	108
citation_issue	1
citation_firstpage	101
citation_lastpage	114
citation_doi	https://doi.org/10.1007/s00233-024-10414-0
citation_public_url	https://hdl.handle.net/11094/95020

Difference of Hilbert series of homogeneous monoid algebras and their normalizations

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