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Bounds on the Castelnuovo-Mumford regularity of tensor products

Author: Giulio Caviglia
Journal: Proc. Amer. Math. Soc. 135 (2007), 1949-1957
MSC (2000): Primary 13D45, 13D02
Published electronically: February 16, 2007
MathSciNet review: 2299466
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Abstract: In this paper we show how, given a complex of graded modules and knowing some partial Castelnuovo-Mumford regularities for all the modules in the complex and for all the positive homologies, it is possible to get a bound on the regularity of the zero homology. We use this to prove that if $ \dim \operatorname{Tor} _1^R(M,N)\leq1$, then $ \operatorname{reg}(M\otimes N)\leq \operatorname{reg}( M)+\operatorname{reg}(N)$, generalizing results of Chandler, Conca and Herzog, and Sidman. Finally we give a description of the regularity of a module in terms of the postulation numbers of filter regular hyperplane restrictions.

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Giulio Caviglia
Affiliation: Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840

Keywords: Castelnuovo-Mumford regularity, postulation number, filter-regular sequence
Received by editor(s): March 3, 2003
Received by editor(s) in revised form: February 1, 2005
Published electronically: February 16, 2007
Additional Notes: The author was partially supported by the “Istituto Nazionale di Alta Matematica Francesco Severi”, Rome
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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