Alexander Duality for Monomial Ideals and Their Resolutions
Abstract
Alexander duality has, in the past, made its way into commutative algebra through StanleyReisner rings of simplicial complexes. This has the disadvantage that one is limited to squarefree monomial ideals. The notion of Alexander duality is generalized here to arbitrary monomial ideals. It is shown how this duality is naturally expressed by Bass numbers, in their relations to the Betti numbers of a monomial ideal and its Alexander dual. Relative cohomological constructions on cellular complexes are shown to relate cellular free resolutions of a monomial ideal to free resolutions of its Alexander dual ideal. As an application, a new canonical resolution for monomial ideals is constructed.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1998
 DOI:
 10.48550/arXiv.math/9812095
 arXiv:
 arXiv:math/9812095
 Bibcode:
 1998math.....12095M
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Combinatorics;
 13D02;
 13P10
 EPrint:
 37 pages, LaTeX, 8 eps figures. Also available at http://math.berkeley.edu/~enmiller