Free resolutions fo rmultigraded modules: a generalization of Taylor's construction
| dc.creator | Charalambous, H. | |
| dc.creator | Tchernev, A. | |
| dc.date | 2002-07-03 | |
| dc.date.accessioned | 2026-07-07T04:49:32Z | |
| dc.date.available | 2026-07-07T04:49:32Z | |
| dc.description | Let $Q=k[x_1,..., x_n]$ be a polynomial ring over a field $k$ with the standard $N^n$-grading. Let $ϕ$ be a morphism of finite free $N^n$-graded $Q$-modules. We translate to this setting several notions and constructions that appear originally in the context of monomial ideals. First, using a modification of the Buchsbaum-Rim complex, we construct a canonical complex $T_\bullet(ϕ)$ of finite free $N^n$-graded $Q$-modules that generalizes Taylor's resolution. This complex provides a free resolution for the cokernel $M$ of $ϕ$ when $ϕ$ satisfies certain rank criteria. We also introduce the Scarf complex of $ϕ$, and a notion of ``generic'' morphism. Our main result is that the Scarf complex of $ϕ$ is a minimal free resolution of $M$ when $ϕ$ is minimal and generic. Finally, we introduce the LCM-lattice for $ϕ$ and establish its significance in determining the minimal resolution of $M$. | |
| dc.description | LaTeX, 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0207040 | |
| dc.identifier | http://arxiv.org/abs/math/0207040 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64455 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D02; 13C05 | |
| dc.title | Free resolutions fo rmultigraded modules: a generalization of Taylor's construction | |
| dc.type | text |