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Bounds on the Castelnuovo-Mumford regularity of tensor products

Giulio Caviglia
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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 $\dim \tor_1^R(M,N)\leq1$ then $\reg(M\otimes N)\leq \reg(M)+\reg(N)$, 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. 2005-10-18. Bounds on the Castelnuovo-Mumford regularity of tensor products. https://arxiv.org/abs/math/0510395

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