Let
be a triangulated homology ball whose boundary complex is
. A
result of Hochster asserts that the canonical module of the Stanley–Reisner ring
of
is isomorphic to the
Stanley–Reisner module
of the pair
.
This result implies that an Artinian reduction of
is (up to
a shift in grading) isomorphic to the Matlis dual of the corresponding Artinian reduction
of
. We
establish a generalization of this duality to all triangulations of connected orientable
homology manifolds with boundary. We also provide an explicit algebraic interpretation of
the
-numbers
of Buchsbaum complexes and use it to prove the monotonicity of
-numbers
for pairs of Buchsbaum complexes as well as the unimodality of
-vectors of barycentric
subdivisions of Buchsbaum polyhedral complexes. We close with applications to the algebraic
manifold
-conjecture.
We have not been able to recognize your IP address
34.239.167.149
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.