General sheaves over weighted projective lines

2005/12/04 by Crawley-Boevey, William
#14H60 (Primary) 16G20 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0512079

Abstract

We develop a theory of general sheaves over weighted projective lines. We define and study a canonical decomposition, analogous to Kac's canonical decomposition for representations of quivers, study subsheaves of a general sheaf, general ranks of morphisms, and prove analogues of Schofield's results on general representations of quivers. Using these, we give a recursive algorithm for computing properties of general sheaves. Many of our results are proved in a more abstract setting, involving a hereditary abelian category.

Related

• Introduction to coherent sheaves on weighted projective lines
• Weighted projective lines as fine moduli spaces of quiver representations
• Thick subcategories on weighted projective curves and nilpotent representations of quivers
• Prüfer sheaves and generic sheaves over the weighted projective lines and elliptic curves
• Quiver algebras, weighted projective lines, and the Deligne-Simpson problem