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 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.

23 pages. Accepted for publication in SCIENCE CHINA Mathematics

References in corpus (2)

• Cluster structures for 2-Calabi-Yau categories and unipotent groups
• Acyclic Calabi-Yau categories

Cited by in corpus (1)

• On tubular tilting objects in the stable category of vector bundles