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arXiv · 1003.4008

Alexander duality and Stanley depth of multigraded modules

Ryota Okazaki·Kohji Yanagawa
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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.

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Ryota Okazaki, Kohji Yanagawa. 2011-02-01. Alexander duality and Stanley depth of multigraded modules. https://arxiv.org/abs/1003.4008

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