Tilting and cluster-tilting objects on weighted projective lines

In this paper, weinvestigate tilting objects and cluster-tilting objects in the categories associated with weighted projective lines. For the case of genus one, tilting objects in the stable category of vector bundles are proved to be precisely cluster-tilting objects in the associated cluster category. Particularly, cluster-tilting objects in the associated cluster category are induced by tilting sheaves in the category of coherent sheaves.