On the regularity of products and intersections of complete intersections
On the regularity of products and intersections of complete intersections
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.