We study the derived category of a complete intersection X of bilinear divisors in the orbifold Sym P(V ). Our results are in the spirit of Kuznetsov’s theory of homological projective duality, and we describe a homological projective duality relation between Sym P(V ) and a category of modules over a sheaf of Clifford algebras on P(Sym V ∨). The proof follows a recently developed strategy combining variation of GIT stability and categories of global matrix factorisations. We begin by translating Db(X) into a derived category of factorisations on an LG model, and then apply VGIT to obtain a birational LG model. Finally, we interpret the derived factorisation category of the new LG model as a Clifford module category. In some cases we can compute this Clifford module category as the derived category of a variety. As a corollary we get a new proof of a result of Hosono and Takagi, which says that a certain pair of nonbirational Calabi–Yau 3-folds have equivalent derived categories.

中文翻译：

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的同调射影对偶

我们研究了 orbifold Sym P(V ) 中双线性因数的完全交集 X 的派生类别。我们的结果本着 Kuznetsov 同调射影对偶理论的精神，我们描述了 Sym P(V ) 与 P(Sym V ∨) 上的一组 Clifford 代数上的一类模之间的同调射影对偶关系。证明遵循最近开发的策略，结合了 GIT 稳定性的变化和全局矩阵分解的类别。我们首先将 Db(X) 转换为 LG 模型上的因式分解的派生类别，然后应用 VGIT 来获得双有理 LG 模型。最后，我们将新 LG 模型的派生因式分解类别解释为 Clifford 模块类别。在某些情况下，我们可以计算这个 Clifford 模块类别作为一个品种的派生类别。