We show that there exists a cubic threefold defined by an invertible polynomial that, when quotiented by the maximal diagonal symmetry group, has a derived category that does not have a full exceptional collection consisting of line bundles. This provides a counterexample to a conjecture of Lekili and Ueda.
Bibliographical notePublisher Copyright:
© The Author(s), 2020. Published by Cambridge University Press.
- Derived categories
- Exceptional collections
- Tilting object