Bezout's theorem and Cohen-Macaulay modules

Migliore, J.; Nagel, U.; Peterson, C.

Bezout's theorem and Cohen-Macaulay modules

Authors

Migliore, J.

Nagel, U.

Peterson, C.

Description

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.
18 pages