2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138544We 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.26 pages; one reference added and a change of notationAlgebraic Geometry14H60 (Primary) 16G20 (Secondary)text