Cayley平面与F型余伴随Grassmann流形的导出范畴
Derived categories of the Cayley plane and the coadjoint Grassmannian of type F
AI总结：
本文证明Faenzi–Manivel的Cayley平面完整Lefschetz例外集限制到其F₄型超平面截面后仍完整，并刻画剩余范畴，给出F型齐性簇的首个完整例外集。
摘要：
对于Cayley平面（即Dynkin型E₆的次微小Grassmann流形）的导出范畴，Faenzi和Manivel构造了一个完整的Lefschetz例外集。Cayley平面的一般超平面截面是Dynkin型F₄的余伴随Grassmann流形。我们证明，将Faenzi–Manivel例外集限制到这样的超平面截面上会给出一个完整的Lefschetz例外集，从而提供了Dynkin型F的齐性簇上完整例外集的首个例子。我们还描述了这些Lefschetz集合的剩余范畴，证实了第二和第三署名作者关于Cayley平面及其超平面截面的猜想。后一描述基于一个具有独立意义的一般性结果，该结果将一个簇与其超平面截面的剩余范畴联系起来。
英文摘要：
For the derived category of the Cayley plane, which is the cominuscule Grassmannian of Dynkin type $\mathrm{E}_6$, a full Lefschetz exceptional collection was constructed by Faenzi and Manivel. A general hyperplane section of the Cayley plane is the coadjoint Grassmannian of Dynkin type $\mathrm{F}_4$. We show that the restriction of the Faenzi-Manivel collection to such a hyperplane section gives a full Lefschetz exceptional collection, providing the first example of a full exceptional collection on a homogeneous variety of Dynkin type $\mathrm{F}$. We also describe the residual categories of these Lefschetz collections, confirming conjectures of the second and third named author for the Cayley plane and its hyperplane section. The latter description is based on a general result of independent interest, relating residual categories of a variety and its hyperplane section.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
