Derived Categories of Families of Sextic del Pezzo Surfaces
Derived Categories of Families of Sextic del Pezzo Surfaces
复制标题
Sextic del Pezzo 曲面族的派生范畴
DOI：
10.1093/imrn/rnz081
复制
发表时间：
2017
影响因子：
1
通讯作者：
A. Kuznetsov
中科院分区：
文献类型：
--
作者：
A. Kuznetsov
We construct a natural semiorthogonal decomposition for the derived category of an arbitrary flat family of sextic del Pezzo surfaces with at worst du Val singularities. This decomposition has three components equivalent to twisted derived categories of finite flat schemes of degrees 1, 3, and 2 over the base of the family. We provide a modular interpretation for these schemes and compute them explicitly in a number of standard families. For two such families the computation is based on a symmetric version of homological projective duality for ${{\mathbb{P}}}^2 \times{{\mathbb{P}}}^2$ and ${{\mathbb{P}}}^1 \times{{\mathbb{P}}}^1 \times{{\mathbb{P}}}^1$, which we explain in an appendix.
We construct a natural semiorthogonal decomposition for the derived category of an arbitrary flat family of sextic del Pezzo surfaces with at worst du Val singularities. This decomposition has three components equivalent to twisted derived categories of finite flat schemes of degrees 1, 3, and 2 over the base of the family. We provide a modular interpretation for these schemes and compute them explicitly in a number of standard families. For two such families the computation is based on a symmetric version of homological projective duality for ${{\mathbb{P}}}^2 \times{{\mathbb{P}}}^2$ and ${{\mathbb{P}}}^1 \times{{\mathbb{P}}}^1 \times{{\mathbb{P}}}^1$, which we explain in an appendix.
影响因子：
1.8
作者：
Hacking, Paul;Prokhorov, Yuri
通讯作者：
Prokhorov, Yuri
关于 Fourier-Mukai 变换的附加
影响因子：
1.7
作者：
Anno R
通讯作者：
Anno R