Bounds on the Castelnuovo-Mumford regularity of tensor products
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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 $\dim \operatorname {Tor} _1^R(M,N)\leq 1$, 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.References
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Additional Information
- Giulio Caviglia
- Affiliation: Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840
- Email: caviglia@math.berkeley.edu
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1949-1957
- MSC (2000): Primary 13D45, 13D02
- DOI: https://doi.org/10.1090/S0002-9939-07-08222-6
- MathSciNet review: 2299466