Monomial Resolutions
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
Call a monomial ideal M "generic" if no variable appears with the same nonzero exponent in two distinct monomial generators. Using a convex polytope first studied by Scarf, we obtain a minimal free resolution of M. Any monomial ideal M can be made generic by deformation of its generating exponents. Thus, the above construction yields a (usually nonminimal) resolution of M for arbitrary monomial ideals, bounding the Betti numbers of M in terms of the Upper Bound Theorem for Convex Polytopes.
We show that our resolutions are DG-algebras, and consider realizability questions and irreducible decompositions.
plain TeX, 20 pages with 5 figures, Postscript file available from ftp://math.columbia.edu/pub/bayer/monomial_resolutions/monres.ps
plain TeX, 20 pages with 5 figures, Postscript file available from ftp://math.columbia.edu/pub/bayer/monomial_resolutions/monres.ps