For the derived category of the Cayley plane, which is the cominuscule Grassmannian of Dynkin type E₆, 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 F₄. 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 F.

中文翻译：

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F型的Cayley飞机和Coadjoint Grassmannian的派生类别

对于Cayley飞机的派生类别，即Dynkin型E ₆的共生草曼，由Faenzi和Manivel构建了一个完整的Lefschetz特殊收藏品。Cayley平面的一般超平面截面是Dynkin类型F ₄的共伴格拉斯曼式。我们证明了Faenzi-Manivel集合对这样一个超平面部分的限制给出了一个完整的Lefschetz例外集合，提供了Dynkin F型同质品种的一个完全例外集合的第一个例子。