Regularity bounds for Koszul cycles

Aldo Conca; Satoshi Murai

doi:10.1090/S0002-9939-2014-12292-1

Regularity bounds for Koszul cycles

Aldo Conca^*, Satoshi Murai

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We study the Castelnuovo-Mumford regularity of the module of Koszul cycles Z_t(I,M) of a homogeneous ideal I in a polynomial ring S with respect to a graded module M in the homological position t ∈ N. Under mild assumptions on the base field we prove that reg Z_t(I,S) is a subadditive function of t when dim S/I = 0. For Borel-fixed ideals I, J we prove that reg Z_t(I,S/J) ≤ t(1 + reg I) + regS/J, a result already announced by Bruns, Conca and Römer.

Original language	English
Pages (from-to)	493-503
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-2014-12292-1
Publication status	Published - 2015
Externally published	Yes

Keywords

Castelnuovo-Mumford regularity
Koszul cycles
Koszul homology

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-2014-12292-1

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title = "Regularity bounds for Koszul cycles",

abstract = "We study the Castelnuovo-Mumford regularity of the module of Koszul cycles Zt(I,M) of a homogeneous ideal I in a polynomial ring S with respect to a graded module M in the homological position t ∈ N. Under mild assumptions on the base field we prove that reg Zt(I,S) is a subadditive function of t when dim S/I = 0. For Borel-fixed ideals I, J we prove that reg Zt(I,S/J) ≤ t(1 + reg I) + regS/J, a result already announced by Bruns, Conca and R{\"o}mer.",

keywords = "Castelnuovo-Mumford regularity, Koszul cycles, Koszul homology",

author = "Aldo Conca and Satoshi Murai",

note = "Publisher Copyright: {\textcopyright} 2014 American Mathematical Society.",

year = "2015",

doi = "10.1090/S0002-9939-2014-12292-1",

language = "English",

volume = "143",

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T1 - Regularity bounds for Koszul cycles

AU - Conca, Aldo

AU - Murai, Satoshi

PY - 2015

Y1 - 2015

N2 - We study the Castelnuovo-Mumford regularity of the module of Koszul cycles Zt(I,M) of a homogeneous ideal I in a polynomial ring S with respect to a graded module M in the homological position t ∈ N. Under mild assumptions on the base field we prove that reg Zt(I,S) is a subadditive function of t when dim S/I = 0. For Borel-fixed ideals I, J we prove that reg Zt(I,S/J) ≤ t(1 + reg I) + regS/J, a result already announced by Bruns, Conca and Römer.

AB - We study the Castelnuovo-Mumford regularity of the module of Koszul cycles Zt(I,M) of a homogeneous ideal I in a polynomial ring S with respect to a graded module M in the homological position t ∈ N. Under mild assumptions on the base field we prove that reg Zt(I,S) is a subadditive function of t when dim S/I = 0. For Borel-fixed ideals I, J we prove that reg Zt(I,S/J) ≤ t(1 + reg I) + regS/J, a result already announced by Bruns, Conca and Römer.

KW - Castelnuovo-Mumford regularity

KW - Koszul cycles

KW - Koszul homology

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DO - 10.1090/S0002-9939-2014-12292-1

M3 - Article

AN - SCOPUS:84919362769

SN - 0002-9939

VL - 143

SP - 493

EP - 503

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

Regularity bounds for Koszul cycles

Abstract

Keywords

ASJC Scopus subject areas

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