A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles
arXiv:2004.04982
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 which does not have a full exceptional collection consisting of line bundles. This provides a counterexample to a conjecture of Lekili and Ueda.
8 pages, minor revision, to appear in Forum of Math, Sigma