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.

中文翻译：

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一个最大分级的可逆三次三次，它不允许完整的特殊线束集合

我们证明存在一个由可逆多项式定义的三次三次，当它被最大对角对称群商时，具有一个派生类别，该类别不具有由线束组成的完整异常集合。这为 Lekili 和 Ueda 的猜想提供了一个反例。