Monomial resolutions
Dave Bayer,
Irena Peeva,
Bernd Sturmfels
Math. Res. Lett.
5 (1998), no. 1-2, 31-46
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.
Source files:
figA.eps
figB.eps
figC.eps
figD.eps
figE.eps
monres.tex
Monomial_BPS98.ps
Monomial_BPS98.pdf
Note: Preprint and source files may not correspond exactly to the published paper.