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

Jianmin Chen, Yanan Lin, Pin Liu, Shiquan Ruan

Published 2013-03-06, updated 2019-04-04Version 4

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 cluster tilting mutation. Moreover, the cluster tilting approach also provides a new method to classify the endomorphism algebras of tilting objects in the category of coherent sheaves and the associated bounded derived category.