1998/04/08 by Dave Bayer, Bayer, Dave, Hara Charalambous +3 · 2 citations
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC
paper · pdf · doi:10.48550/arxiv.math/9804052
Minor revision. 15 pages, Plain TeX with epsf.tex, 8 PostScript figures, PostScript file available also at http://www.math.columbia.edu/~psorin/eprints/monbetti.ps
arxiv created 1998/10/15 · arxiv updated 2009/11/30
In this short note 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.