Tilting objects on tubular weighted projective lines: A cluster tilting approach

Using the cluster tilting theory,we investigate the tilting objects in the stable category of vector bundles on a weighted projective line of weight type(2,2,2,2).More precisely,a tilting object consisting of rank-two bundles is constructed via the cluster tilting mutation.Moreover,the cluster tilting approach also provides a new method to classify the endomorphism algebras of the tilting objects in the category of coherent sheaves and the associated bounded derived category.

Classification of tilting bundles over a weighted projective line of type （2, 3, 3）

We give a complete classification of tilting bundles over a weighted projective line of type （2, 3, 3）. This yields another realization of the tame concealed algebras of type E6.

Prüfer Sheaves and Generic Sheaves Over the Weighted Projective Lines and Elliptic Curves

In the present paper, we introduce the concepts of Prüfer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prüfer sheaves and adic sheaves can characterize the category of coherent sheaves. Moreover, we describe the relationship between Prüfer sheaves and generic sheaves, and provide two methods to construct generic sheaves by using coherent sheaves and Prüfer sheaves.

Tilting sheaves for weighted projective lines of weight type （p）

We give a complete classification of tilting sheaves over weighted projective lines of weight type （p）.