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

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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… Click to show full abstract

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: line bundles; full exceptional; cubic threefold; exceptional collection

Journal Title: Forum of Mathematics, Sigma
Year Published: 2020

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