论文标题
镜像对称和福卡亚类别的奇异性超曲面类别
Mirror symmetry and Fukaya categories of singular hypersurfaces
论文作者
论文摘要
我们考虑了Auroux提出的单一超表面的福卡亚类别的定义，该定义是通过将附近纤维的福卡亚类别定位在Seidel的自然转化中，并表明这具有多种理想的特性。首先，我们证明了Orlov衍生的Knörrer周期定理的A侧类似物，表明AUROUX的类别与高维Landau-Ginzburg模型的Fukaya-Seidel类别相当。其次，我们描述了该定义如何意味着某些大型复杂结构限制Abelian品种的同源镜像对称性。
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's category is derived equivalent to the Fukaya-Seidel category of a higher-dimensional Landau-Ginzburg model. Secondly, we describe how this definition implies homological mirror symmetry for some large complex structure limit degenerations of abelian varieties.
