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Derived categories of quintic del Pezzo fibrations
Selecta Mathematica ( IF 1.4 ) Pub Date : 2021-01-07 , DOI: 10.1007/s00029-020-00615-0
Fei Xie

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.



中文翻译:

派生的五重del Pezzo纤维化类别

我们为有理Gorenstein奇点的五次del Pezzo表面的纤维化的派生类别提供半正交分解。存在三个分量,其中两个分量等于基数的派生类别,其余的非平凡分量等效于基数为5的平面有限有限方案的派生类别。我们介绍了两种构造分解的方法。一种是在库兹涅佐夫(Kuznetsov)对性德尔佩索(De Pezzo)纤维化工作之后的模空间方法,其成分由精细相对模空间的衍生类别给出。另一种方法是可以将纤维化作为格拉斯曼束的线性部分并应用同源射影对偶。

更新日期:2021-01-08
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