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

Abstract

Using cluster tilting theory, we investigate 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.