Mirror symmetry and Fukaya categories of singular hypersurfaces
Mirror symmetry and Fukaya categories of singular hypersurfaces
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DOI：
10.1016/j.aim.2021.108116
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发表时间：
2020-12
影响因子：
1.7
通讯作者：
Maxim Jeffs
中科院分区：
文献类型：
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作者：
Maxim Jeffs
我们考虑了 Auroux 提出的奇异超曲面的 Fukaya 范畴的定义，通过在 Seidel 自然变换中本地化附近纤维的 Fukaya 范畴给出，并表明它具有几个理想的属性。首先，我们通过证明 Auroux 范畴与高维 Landau-Ginzburg 模型的 Fukaya-Seidel 范畴等效，证明了 Orlov 导出的 Knörrer 周期性定理的 A 侧模拟。其次，在 Abouzaid-Auroux 和 Abouzaid-Gross-Siebert 即将开展的工作的背景下，我们描述了这个定义如何暗示在各种大型复杂结构极限下的同调镜像对称性。
We consider a definition of the Fukaya category of a singular hypersurface proposed by Auroux, given by localizing the Fukaya category of a nearby fiber at Seidel's natural transformation, and show that this possesses several desirable properties. Firstly, we prove an A-side analog of Orlov's derived Knörrer periodicity theorem by showing that Auroux' category is derived equivalent to the Fukaya-Seidel category of a higher-dimensional Landau-Ginzburg model. Secondly, we describe how this definition should imply homological mirror symmetry at various large complex structure limits, in the context of forthcoming work of Abouzaid-Auroux and Abouzaid-Gross-Siebert.