On the regularity of products and intersections of complete intersections

Chardin, Marc; Minh, Nguyen; Trung, Ngo

doi:10.1090/S0002-9939-06-08842-3

On the regularity of products and intersections of complete intersections
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by Marc Chardin, Nguyen Cong Minh and Ngo Viet Trung

Proc. Amer. Math. Soc. 135 (2007), 1597-1606

DOI: https://doi.org/10.1090/S0002-9939-06-08842-3

Published electronically: December 27, 2006

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Abstract:

This paper proves the formulae \begin{align*} \operatorname {reg}(IJ) & \le \operatorname {reg}(I) + \operatorname {reg}(J), \operatorname {reg}(I \cap J) & \le \operatorname {reg}(I) + \operatorname {reg}(J) \end{align*} for arbitrary monomial complete intersections $I$ and $J$, and provides examples showing that these inequalities do not hold for general complete intersections.

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