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arXiv · alg-geom/9610012

Monomial Resolutions

Dave Bayer·Irena Peeva·Bernd Sturmfels
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Abstract

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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BibTeXRIS

Dave Bayer, Irena Peeva, Bernd Sturmfels. 1996-10-11. Monomial Resolutions. https://arxiv.org/abs/alg-geom/9610012

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