Abstract:Weighted projective lines are introduced by Geigle-Lenzing which give a geometric treatment to the representation theory of the canonical algebras. The study of weighted projective lines is closely related to canonical algebras, cluster algebras, compact Riemann surfaces, Hall algebras and quantum algebras, singularity theory, GL order, and so on. In this talk, I will introduce the notion of weighted projective lines, describe the structure of coherent sheaves category over a weighted projective line and show our work on weighted projective lines.