2004/05/28 by Roberto Martínez-Villa, Roberto Martinez-Villa, Martinez-Villa, Roberto
Mathematics · Physics and Astronomy · #14 #16 #18 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.AG #math.RT #msc:14 #msc:16 #msc:18
paper · pdf · doi:10.48550/arxiv.math/0405538
arxiv created 2004/05/28 · openalex publication_date 2004/05/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We are going to show that the sheafication of graded Koszul modules % KΓ over Γn=K[ x0,x1...xn] form an important subcategory \overset\wedgeKΓ of the coherents sheaves on projective space, Coh(Pn). One reason is that any coherent sheave over Pn belongs to \overset\wedgeKΓup to shift. More importantly, the category KΓ 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 Coh(Pn), with respect to this theory, all but finitely many Auslander-Reiten components for Coh(Pn) have the shape ZA∞. We also describe the remaining ones.