Derived categories of quintic del Pezzo fibrations
Derived categories of quintic del Pezzo fibrations
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五次 del Pezzo 纤维的派生类别
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发表时间：
2020
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通讯作者：
F. Xie
中科院分区：
文献类型：
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作者：
F. Xie
我们为具有有理 Gorenstein 奇点的五次 del Pezzo 表面的纤维化的派生类别提供了半正交分解。共有三个分量，其中两个等效于基的派生类别，其余的非平凡分量等效于基上平坦且有限的 5 次方案的派生类别。我们介绍两种构造分解的方法。一种是模空间方法，遵循库兹涅佐夫关于六次德尔佩佐纤维的工作，并且组件由精细相对模空间的派生类别给出。另一种方法是可以将纤维化实现为格拉斯曼丛的线性部分并应用同调射影对偶性。
We provide a semiorthogonal decomposition for the derived category of fibrations of quintic del Pezzo surfaces with rational Gorenstein singularities. There are three components, two of which are equivalent to the derived categories of the base and the remaining non-trivial component is equivalent to the derived category of a flat and finite of degree 5 scheme over the base. We introduce two methods for the construction of the decomposition. One is the moduli space approach following the work of Kuznetsov on the sextic del Pezzo fibrations and the components are given by the derived categories of fine relative moduli spaces. The other approach is that one can realize the fibration as a linear section of a Grassmannian bundle and apply homological projective duality.