Sequentially Cohen--Macaulay modules with respect to an irrelevant ideal

Details Sequentially Cohen--Macaulay modules with respect to an irrelevant ideal Sequentially Cohen--Macaulay modules with respect to an irrelevant ideal

2011-12-16

arxiv.org/abs/1112.3717v1

Mathematics

Commutative Algebra

Scientific paper

For a finitely generated bigraded $S$-module $M$ where $S$ is a standard bigraded polynomial ring we define the relative Cohen--Macaulay filtration $\mathcal{F}$ of $M$ with respect to the bigraded irrelevant ideal $Q$. We call $M$ to be sequentially Cohen-Macaulay with respect $Q$ if $M$ admits a relative Cohen-Macaulay filtration with respect to $Q$. We investigate the algebraic properties of these modules and compute the length of a relative Cohen-Macaulay filtration with respect to $Q$ explicitly. All hypersurface rings that are sequentially Cohen--Macaulay with respect to $Q$ are classified.

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