Alexander Duality and Serre's Property $(S_i)$ for Square-free Monomial Ideals
| dc.creator | Kummini, Manoj | |
| dc.date | 2007-09-01 | |
| dc.date | 2007-12-04 | |
| dc.date.accessioned | 2026-07-07T08:46:38Z | |
| dc.date.available | 2026-07-07T08:46:38Z | |
| dc.description | In this note, we study Serre's property $(S_i)$, and its relation to Alexander duality for monomial ideals in a polynomial ring over a field. We describe ideals that define the non-Cohen-Macaulay- and the non-$(S_i)$-loci of finitely generated modules over regular rings, and show that minimal prime ideals in these loci are homogeneous, in the graded case. We show that a square-free monomial ideal has property $(S_i)$ if and only if its Alexander dual has a linear resolution up to homological degree $i-1$. We prove that for square-free monomial ideals, having property $(S_2)$ is equivalent to being locally connected in codimension 1. | |
| dc.description | Withdrawn by the author as it was learnt that this result was earlier proved by K. Yanagawa, J. Algebra, vol. 225, no. 2, 2000 | |
| dc.identifier | https://arxiv.org/abs/0709.0031 | |
| dc.identifier | http://arxiv.org/abs/0709.0031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143312 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13F55, 13D02 (Primary) | |
| dc.title | Alexander Duality and Serre's Property $(S_i)$ for Square-free Monomial Ideals | |
| dc.type | text |