Monomial Resolutions

Details Monomial Resolutions Monomial Resolutions

1996-10-11

arxiv.org/abs/alg-geom/9610012v1

Mathematics

Algebraic Geometry

plain TeX, 20 pages with 5 figures, Postscript file available from ftp://math.columbia.edu/pub/bayer/monomial_resolutions/monr

Scientific paper

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.

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