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Regularity bounds for Koszul cycles


Authors: Aldo Conca and Satoshi Murai
Journal: Proc. Amer. Math. Soc. 143 (2015), 493-503
MSC (2010): Primary 13D02, 13D03
DOI: https://doi.org/10.1090/S0002-9939-2014-12292-1
Published electronically: October 24, 2014
MathSciNet review: 3283639
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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\in {\mathbb{N}}$. Under mild assumptions on the base field we prove that $ \operatorname {reg} Z_t(I,S)$ is a subadditive function of $ t$ when $ \operatorname {dim} S/I=0$. For Borel-fixed ideals $ I,J$ we prove that $ \operatorname {reg} Z_t(I,S/J)\leq t(1+ \operatorname {reg} I)+\operatorname {reg} S/J$, a result already announced by Bruns, Conca and Römer.


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Additional Information

Aldo Conca
Affiliation: Dipartimento di Matematica, Universitá di Genova, Via Dodecaneso 35, 16146 Genova, Italy
Email: conca@dima.unige.it

Satoshi Murai
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 560-0043, Japan
Email: s-murai@ist.osaka-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2014-12292-1
Keywords: Castelnuovo-Mumford regularity, Koszul cycles, Koszul homology
Received by editor(s): October 11, 2012
Received by editor(s) in revised form: May 2, 2013
Published electronically: October 24, 2014
Additional Notes: The research of the second author was partially supported by KAKENHI 22740018
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.