A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles

Abstract

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.

Keywords

• exceptional collections
• derived categories
• tilting object
• 14F08