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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm113-1-8,
author = {William Crawley-Boevey},
title = {General sheaves over weighted projective lines},
journal = {Colloquium Mathematicae},
volume = {111},
year = {2008},
pages = {119-149},
zbl = {1148.14015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm113-1-8}
}
William Crawley-Boevey. General sheaves over weighted projective lines. Colloquium Mathematicae, Tome 111 (2008) pp. 119-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm113-1-8/