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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Regularity bounds for Koszul cycles
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by Aldo Conca and Satoshi Murai PDF
Proc. Amer. Math. Soc. 143 (2015), 493-503 Request permission


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
  • MR Author ID: 335439
  • Email:
  • Satoshi Murai
  • Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 560-0043, Japan
  • MR Author ID: 800440
  • Email:
  • 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
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 493-503
  • MSC (2010): Primary 13D02, 13D03
  • DOI:
  • MathSciNet review: 3283639