Rigid resolutions and big Betti numbers
| dc.creator | Conca, Aldo | |
| dc.creator | Herzog, Juergen | |
| dc.creator | Hibi, Takayuki | |
| dc.date | 2003-06-16 | |
| dc.date.accessioned | 2026-07-07T04:58:59Z | |
| dc.date.available | 2026-07-07T04:58:59Z | |
| dc.description | In the first part of the paper we answer (positively) a question raised by the first author which has to do with some sort of rigity of the tail of resolution of an ideal. Let $I$ be a homogeneous ideal in a polynomial ring over a field of characteristic 0. Denote by $β_i(I)$ the $i$-th Betti number of $I$ and by $Gin(I)$ the revlex generic initial ideal of $I$. In general one has $β_i(I)\leq β_i(Gin(I))$ and we show that if $β_i(I)=β_i(Gin(I))$ for some $i$ then $β_j(I)=β_j(Gin(I))$ for all $j>i$. In the second part of the paper we answer a question of Eisenbud and Huneke. We prove that if $I$ is $m$-primary and $I\subset m^d$ then $β_i(m^d)\leq β_i(Gin(I))$ for all $i$. | |
| dc.identifier | https://arxiv.org/abs/math/0306236 | |
| dc.identifier | http://arxiv.org/abs/math/0306236 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67801 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D02 | |
| dc.title | Rigid resolutions and big Betti numbers | |
| dc.type | text |