5,624 research outputs found
Castelnuovo-Mumford regularity for complexes and weakly Koszul modules
Let A be a noetherian AS regular Koszul quiver algebra (if A is commutative,
it is essentially a polynomial ring), and grA the category of finitely
generated graded left A-modules. Following Jorgensen, we define the
Castelnuovo-Mumford regularity reg(X) of a complex X \in D^b(grA) in terms of
the local cohomologies or the minimal projective resolution of X. Let A^! be
the quadratic dual ring of A. For the Koszul duality functor DG : D^b(grA) ->
D^b(grA^!), we have reg(X) = max {i | H^i(DG (X)) \ne 0}. Using these concepts,
we study weakly Koszul modules (= componentwise linear modules) over A^!. As an
application, refining a result of Herzog and Roemer, we show that if J is a
monomial ideal of an exterior algebra E= \bigwedge with d
\geq 3, then the (d-2)nd syzygy of E/J is weakly Koszul.Comment: 21 pages, to appear in J. Pure Appl. Algebra, the description of the
"(non-commutative)canonical module" is correcte
Dualizing complex of the face ring of a simplicial poset
A finite poset is called "simplicial", if it has the smallest element
, and every interval is a boolean algebra. The face
poset of a simplicial complex is a typical example. Generalizing the
Stanley-Reisner ring of a simplicial complex, Stanley assigned the graded ring
to . 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 , which has many applications.Comment: 16 pages. Simplified the proof of the main theorem. Added the remark
that a theorem of Murai-Terai also holds for simplicial posets
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