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General sheaves over weighted projective lines

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Crawley-Boevey W.

Colloquium Mathematicum

2008

tom 113

nr 1

119-149

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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1 Colloquium Mathematicum

1 Crawley-Boevey W.

1 2008

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General sheaves over weighted projective lines