论文标题
Cayley飞机的派生类别和F型的Coadhinchanchoint Grassmannian
Derived categories of the Cayley plane and the coadjoint Grassmannian of type F
论文作者
论文摘要
对于Cayley Plane的派生类别，这是Dynkin型$ \ Mathrm {E} _6 $的Cominuscule Grassmannian，由Faenzi和Manivel构建了一个完整的Lefschetz出色收藏。 Cayley平面的一般超平面部分是Dynkin型$ \ Mathrm {F} _4 $的Coadjoint Grassmannian。我们表明，Faenzi-Manivel收集到这样的超平面部分的限制提供了一个完整的Lefschetz出色集合，这是第一个在均质的Dynkin Type $ \ Mathrm {F} $上进行完整的特殊集合的第一个例子。 我们还描述了这些Lefschetz集合的残差类别，证实了第二和第三名的猜想，名为Cayley Plane及其超平面部分的作者。后一个描述基于独立兴趣的一般结果，将多样性的残差类别及其超平面部分关联。
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.
