Koszul Algebras and Sheaves over Projective Space
| dc.creator | Martinez-Villa, Roberto | |
| dc.date | 2004-05-28 | |
| dc.date.accessioned | 2026-07-07T05:08:40Z | |
| dc.date.available | 2026-07-07T05:08:40Z | |
| dc.description | We are going to show that the sheafication of graded Koszul modules $% K_Γ$ over $Γ_{n}=K[ x_{0},x_{1}...x_{n}] $ form an important subcategory $\overset{\wedge}{K}_Γ$ of the coherents sheaves on projective space, $Coh(P^{n}).$ One reason is that any coherent sheave over $P^{n}$ belongs to $\overset{\wedge}{K}_Γ$up to shift. More importantly, the category $K_Γ$ allows a concept of almost split sequence obtained by exploiting Koszul duality between graded Koszul modules over $Γ$ and over the exterior algebra $Λ.$ This is then used to develop a kind of relative Auslander-Reiten theory for the category $\mathit{Coh(P}^{n})$, with respect to this theory, all but finitely many Auslander-Reiten components for $\mathit{Coh(P}^{n})$ have the shape \textit{ZA}$_{\infty}.$ We also describe the remaining ones. | |
| dc.identifier | https://arxiv.org/abs/math/0405538 | |
| dc.identifier | http://arxiv.org/abs/math/0405538 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71356 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14, 16, 18 | |
| dc.title | Koszul Algebras and Sheaves over Projective Space | |
| dc.type | text |