Consecutive cancellations in Betti numbers of local rings
| dc.creator | Rossi, Maria Evelina | |
| dc.creator | Sharifan, Leila | |
| dc.date | 2009-04-07 | |
| dc.date.accessioned | 2026-07-07T13:01:16Z | |
| dc.date.available | 2026-07-07T13:01:16Z | |
| dc.description | Let I be a homogeneous ideal in a polynomial ring P over a field. By Macaulay's Theorem, there exists a lexicographic ideal L=Lex(I) with the same Hilbert function as I. Peeva has proved that the Betti numbers of P/I can be obtained from the graded Betti numbers of P/L by a suitable sequence of consecutive cancellations. We extend this result to any ideal I in a regular local ring (R,m) by passing through the associated graded ring. To this purpose it will be necessary to enlarge the list of the allowed cancellations. Taking advantage of Eliahou-Kervaire's construction, several applications are presented. This connection between the graded perspective and the local one is a new viewpoint and we hope it will be useful for studying the numerical invariants of classes of local rings. | |
| dc.description | 12 pages, to appear in Proc. AMS | |
| dc.identifier | https://arxiv.org/abs/0904.1086 | |
| dc.identifier | http://arxiv.org/abs/0904.1086 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226098 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13D02 | |
| dc.title | Consecutive cancellations in Betti numbers of local rings | |
| dc.type | text |