Geodesic
A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles
Forum of Mathematics, Sigma, Tome 8 (2020)

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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. 
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     author = {David Favero and Daniel Kaplan and Tyler L. Kelly},
     title = {A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles},
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David Favero; Daniel Kaplan; Tyler L. Kelly. A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.44

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