Koszul Algebras and Sheaves over Projective Space

dc.creatorMartinez-Villa, Roberto
dc.date2004-05-28
dc.date.accessioned2026-07-07T05:08:40Z
dc.date.available2026-07-07T05:08:40Z
dc.descriptionWe 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.identifierhttps://arxiv.org/abs/math/0405538
dc.identifierhttp://arxiv.org/abs/math/0405538
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71356
dc.subjectRepresentation Theory
dc.subjectAlgebraic Geometry
dc.subject14, 16, 18
dc.titleKoszul Algebras and Sheaves over Projective Space
dc.typetext

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