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Bezout's theorem and Cohen-Macaulay modules

J. Migliore·U. Nagel·C. Peterson
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Abstract

We define very proper intersections of modules and projective subschemes. It turns out that equidimensional locally Cohen-Macaulay modules intersect very properly if and only if they intersect properly. We prove a Bezout theorem for modules which meet very properly. Furthermore, we show for equidimensional subschemes $X$ and $Y$: If they intersect properly in an arithmetically Cohen-Macaulay subscheme of positive dimension then $X$ and $Y$ are arithmetically Cohen-Macaulay. The module version of this result implies splitting criteria for reflexive sheaves.

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J. Migliore, U. Nagel, C. Peterson. 1999-07-12. Bezout's theorem and Cohen-Macaulay modules. https://arxiv.org/abs/math/9907074

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