Alexander duality and Stanley depth of multigraded modules
Commutative Algebra
2011-02-02 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1003.4008,
title = {Alexander duality and Stanley depth of multigraded modules},
author = {Ryota Okazaki and Kohji Yanagawa},
journal= {arXiv preprint arXiv:1003.4008},
year = {2011}
}
Comments
18 pages. We have removed Lemma 2.3 of the previous version, since the proof contained a gap. This deletion does not affect the main results, while we have revised argument a little (especially in Sections in 2 and 3)