Extremal Betti Numbers and Applications to Monomial Ideals

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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.
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

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Commutative Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/76811

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9804052
 http://arxiv.org/abs/math/9804052

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arXiv