General sheaves over weighted projective lines

Abstract

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.

The dimension of the derived category of elliptic curves and tubular weighted projective lines

“…(1) X is an elliptic curve, or (2) X is a weighted projective line of tubular type, that is, of type (2, 2, 2, 2), (3,3,3), (2,4,4) or (2,3,6)-see [10], in particular [10, 5.4.2] (see also [9] for a study of general sheaves, somewhat related to what we do in this paper).…”