标题： 排列多面体和星形多面体品种的导出范畴 显示英文标题

标题： Derived Categories of Permutahedral and Stellahedral Varieties

摘要： 我们利用相干可构造对应关系，通过由多面体构建的可构造层的组合学，在环面簇的导出范畴中构造了全强例外的拟线丛集合。为了证明序列是全的，我们构建了线丛的精确复形，这些复形对 McMullen 多面体代数中的关系进行分类。我们计算了某些多面体上可构造层之间的同态，并利用此将例外性的提问简化为证明某些多面体的集合差是收缩的。作为我们方法的应用，我们为与排列多面体、星形多面体以及类型$B_n$的 Coxeter 排列多面体相关的环面簇构造了全强例外的拟线丛集合。我们的集合中的线丛分别由无环 Schubert 矩阵的基多面体、所有 Schubert 矩阵的独立多面体以及无环 Schubert delta 矩阵的可行多面体索引。我们的集合满足许多良好的性质：首先，编码倾斜层自同态代数的带关系的图可以以一种对弱映射和矩阵包含概念的轻微扩展的方式从矩阵理论的角度描述；其次，我们的集合在相应扇形的自然对称性下保持不变；最后，导出范畴中诱导的半正交分解细化了 Castravet 和 Tevelev 研究的尖点半正交分解。这给出了一个全强例外的拟线丛集合，用于由无环和无吊环 Schubert 矩阵和 Schubert delta 矩阵索引的我们流形的导出范畴的尖点部分。 显示英文摘要

摘要： We utilize the coherent-constructible correspondence to construct full strongly exceptional collections of nef line bundles in the derived category of a toric variety through the combinatorics of constructible sheaves built from polytopes. To show that sequences are full, we build exact complexes of line bundles that categorify the relations in the McMullen polytope algebra. We compute the homomorphisms between certain constructible sheaves on polytopes and use this to reduce the question of exceptionality to showing that certain set differences of polytopes are contractible. As an application of our method, we construct full strongly exceptional collections of nef line bundles for the toric varieties associated to the permutahedron, stellahedron, and the type $B_n$ Coxeter permutahedron. The line bundles in our collections are indexed by base polytopes of loopless Schubert matroids, independence polytopes of all Schubert matroids, and feasible polytopes of loopless Schubert delta matroids, respectively. Our collections satisfy a number of nice properties: First, the quiver with relations that encodes the endomorphism algebra of the tilting sheaf can be described matroid-theoretically as a slight extension of the notion of weak maps and inclusion of matroids; Second, our collections are invariant under the natural symmetries of the corresponding fans; Finally, the induced semi-orthogonal decomposition of the derived categories refines the cuspidal semi-orthogonal decomposition as studied by Castravet and Tevelev. This gives a full strongly exceptional collection of nef line bundles for the cuspidal parts of the derived categories of our varieties indexed by loopless and coloopless Schubert matroids and Schubert delta matroids.