Bezout's theorem and Cohen-Macaulay modules

J. Migliore, U. Nagel, C. Peterson

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish
Pages (from-to)373-394
Number of pages22
JournalMathematische Zeitschrift
Volume237
Issue number2
DOIs
StatePublished - Jun 2001

ASJC Scopus subject areas

  • General Mathematics

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