Kohji Yanagawa
Alexander duality and Stanley depth of multigraded modules.
Tue, 03/23/2010 - 16:01 — SomNambulAuthors: Kohji Yanagawa, Ryota Okazaki
Subjects: Commutative Algebra
AbstractWe 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 ideals.Higher Cohen-Macaulay property of squarefree modules and simplicial posets.
Thu, 01/21/2010 - 16:01 — SomNambulAuthors: Kohji Yanagawa
Subjects: Commutative Algebra
AbstractRecently, G. Floystad studied "higher Cohen-Macaulay property" of certain
finite regular cell complexes. In this paper, we partially extend his results
to squarefree modules, toric face rings, and simplicial posets. For example, we
show that if (the corresponding cell complex of) a simplicial poset is
$l$-Cohen-Macaulay then its codimension one skeleton is $(l+1)$-Cohen-Macaulay.Dualizing complex of the face ring of a simplicial poset.
Fri, 10/09/2009 - 18:27 — SomNambulAuthors: Kohji Yanagawa
Subjects: Commutative Algebra
AbstractA finite poset $P$ is called "simplicial", if it has the smallest element
$0^$, and every interval $[0^, x]$ is a boolean algebra. The face poset of a
simplicial complex is a typical example. Stanley assigned the graded ring $A_P$
to $P$ generalizing the Stanley-Reisner ring of a simplicial complex. This ring
has been studied from both combinatorial and topological perspective. In this
paper, we will give a concise description of a dualizing complex of $A_P$. As
an application, we will construct the squarefree module theory over $A_P$.
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