A characterization of the hereditary categories derived equivalent to somecategory of coherent sheaves on a weighted projective line

Let H be a connected hereditary abelian category over an algebraically clos ed field k, with finite dimensional homomorphism and extension spaces. Ther e are two main known types of such categories: those derived equivalent to mod lambda for some finite dimensional hereditary k-algebra lambda and thos e derived equivalent to some category coh X of coherent sheaves on a weight ed projective line X in the sense of Geigle and Lenzing (1987). The aim of this paper is to give a characterization of the second class in terms of so me properties known to hold for these hereditary categories.