Alexander duality and Stanley depth of multigraded modules

Details Alexander duality and Stanley depth of multigraded modules Alexander duality and Stanley depth of multigraded modules

2010-03-21

arxiv.org/abs/1003.4008v3

Mathematics

Commutative Algebra

18 pages. We have removed Lemma 2.3 of the previous version, since the proof contained a gap. This deletion does not affect th

Scientific paper

We apply Miller's theory on multigraded modules over a polynomial ring to the study of the Stanley depth of these modules. Several tools for Stanley's conjecture are developed, and a few partial answers are given. For example, we show that taking the Alexander duality twice (but with different "centers") is useful for this subject. Generalizing a result of Apel, we prove that Stanley's conjecture holds for the quotient by a cogeneric monomial ideal.

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