Extremal Betti Numbers and Applications to Monomial Ideals
| dc.creator | Bayer, Dave | |
| dc.creator | Charalambous, Hara | |
| dc.creator | Popescu, Sorin | |
| dc.date | 1998-04-08 | |
| dc.date | 1998-10-15 | |
| dc.date.accessioned | 2026-07-07T05:24:22Z | |
| dc.date.available | 2026-07-07T05:24:22Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/9804052 | |
| dc.identifier | http://arxiv.org/abs/math/9804052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76811 | |
| dc.subject | Commutative Algebra | |
| dc.title | Extremal Betti Numbers and Applications to Monomial Ideals | |
| dc.type | text |