General sheaves over weighted projective lines

Volume 113 / 2008

William Crawley-Boevey Colloquium Mathematicum 113 (2008), 119-149 MSC: Primary 14H60; Secondary 16G20. DOI: 10.4064/cm113-1-8


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.


  • William Crawley-BoeveyDepartment of Pure Mathematics
    University of Leeds
    Leeds LS2 9JT, UK

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