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

Let be a connected hereditary abelian category over an algebraically closed field , with finite dimensional homomorphism and extension spaces. There are two main known types of such categories: those derived equivalent to for some finite dimensional hereditary -algebra and those derived equivalent to some category of coherent sheaves on a weighted projective line 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 some properties known to hold for these hereditary categories.