Alexander duality and Stanley depth of multigraded modules

作者：Okazaki Ryota; Yanagawa Kohji^*

来源：Journal of Algebra, 2011, 340(1): 35-52.

DOI：10.1016/j.jalgebra.2011.05.028

• Stanley depth
• Multigraded module
• Alexander duality functor
• (Co)generic monomial ideal

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.

• 出版日期2011-8-15