General sheaves over weighted projective lines

Details General sheaves over weighted projective lines General sheaves over weighted projective lines

2005-12-04

arxiv.org/abs/math/0512079v2

Mathematics

Algebraic Geometry

26 pages; one reference added and a change of notation

Scientific paper

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.

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