Length Formulas for the Homology of Generalized Koszul Complexes
| dc.creator | Ichim, Bogdan | |
| dc.creator | Vetter, Udo | |
| dc.date | 2005-10-27 | |
| dc.date.accessioned | 2026-07-07T06:48:01Z | |
| dc.date.available | 2026-07-07T06:48:01Z | |
| dc.description | Let $M$ be a finite module over a noetherian ring $R$ with a free resolution of length 1. We consider the generalized Koszul complexes $\mathcal{C}_{\barλ}(t)$ associated with a map $\barλ:M\to\mathcal{H}$ into a finite free $R$-module $\mathcal{H}$ (see [IV], section 3), and investigate the homology of $\mathcal{C}_{\barλ}(t)$ in the special setup when $\grade I_M=\rank M=\dim R$. ($I_M$ is the first non-vanishing Fitting ideal of $M$.) In this case the (interesting) homology of $\mathcal{C}_{\barλ}(t)$ has finite length, and we deduce some length formulas. As an application we give a short algebraic proof of an old theorem due to Greuel (see [G], Proposition 2.5). We refer to [HM] where one can find another proof by similar methods. | |
| dc.identifier | https://arxiv.org/abs/math/0510608 | |
| dc.identifier | http://arxiv.org/abs/math/0510608 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103847 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13D25 | |
| dc.title | Length Formulas for the Homology of Generalized Koszul Complexes | |
| dc.type | text |