Betti numbers of determinantal ideals
| dc.creator | Miró-Roig, Rosa M. | |
| dc.date | 2007-01-16 | |
| dc.date.accessioned | 2026-07-07T07:41:17Z | |
| dc.date.available | 2026-07-07T07:41:17Z | |
| dc.description | Let $R=k[x_1, ..., x_n]$ be a polynomial ring and let $I\subset R$ be a graded ideal. In \cite{R}, Römer asked whether under the Cohen-Macaulay assumption the $i$-th Betti number $β_{i}(R/I)$ can be bounded above by a function of the maximal shifts in the minimal graded free $R$-resolution of $R/I$ as well as bounded below by a function of the minimal shifts. The goal of this paper is to establish such bounds for graded Cohen-Macaulay algebras $k[x_1, ..., x_n]/I$ when $I$ is a standard determinantal ideal of arbitrary codimension. We also discuss other examples as well as when these bounds are sharp. | |
| dc.identifier | https://arxiv.org/abs/math/0701435 | |
| dc.identifier | http://arxiv.org/abs/math/0701435 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122051 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Primary 13H15 13D02; Secondary 14M12 | |
| dc.title | Betti numbers of determinantal ideals | |
| dc.type | text |