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Castelnuovo-Mumford regularity of Koszul cycles and Koszul homologies


Authors: Kamran Lamei and Navid Nemati
Journal: Proc. Amer. Math. Soc. 146 (2018), 2765-2772
MSC (2010): Primary 13D02, 13D03
DOI: https://doi.org/10.1090/proc/13973
Published electronically: February 16, 2018
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Abstract: We extend to one dimensional quotients the result of A. Conca and S. Murai on the convexity of the regularity of Koszul cycles. By providing a relation between the regularity of Koszul cycles and Koszul homologies we prove a sharp regularity bound for the Koszul homologies of a homogeneous ideal in a polynomial ring under the same conditions.


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Kamran Lamei
Affiliation: School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
Email: kamran.lamei@ut.ac.ir

Navid Nemati
Affiliation: School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran — and — Institut de Mathématiques de Jussieu, UPMC, 75005 Paris, France
Email: navid.nemati@imj-prg.fr

DOI: https://doi.org/10.1090/proc/13973
Keywords: Castelnuovo-Mumford regularity, Koszul cycle, Koszul homology
Received by editor(s): May 16, 2017
Received by editor(s) in revised form: September 12, 2017
Published electronically: February 16, 2018
Communicated by: Irena Peeva
Article copyright: © Copyright 2018 American Mathematical Society

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