Extremal Betti numbers and applications to monomial ideals
Dave Bayer,
Hara Charalambous,
Sorin Popescu
J. Algebra
221 (1999), no. 2, 497-512
Abstract:
We introduce a notion of extremality for Betti numbers of a minimal
free resolution, which can be seen as a refinement of the notion of
Mumford-Castelnuovo regularity. We show that extremal Betti numbers of
an arbitrary submodule of a free S-module are preserved when taking
the generic initial module. We relate extremal multigraded Betti
numbers in the minimal resolution of a square free monomial ideal with
those of the monomial ideal corresponding to the Alexander dual
simplicial complex and generalize theorems of Eagon-Reiner and Terai.
As an application we give easy (alternative) proofs of classical
criteria due to Hochster, Reisner, and Stanley.
Source files:
onedot.eps
twodots.eps
threedots.eps
fourdots.eps
fivedots.eps
mobius.eps
strange.eps
torus.eps
monbetti.tex
Betti_BCP99.ps
Betti_BCP99.pdf
Note: Preprint and source files may not correspond exactly to the published paper.