Mirror symmetry and Fukaya categories of singular hypersurfaces

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 Knorrer 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.(c) 2021 Elsevier Inc. All rights reserved.

Automated summary

We explore the definition of the Fukaya category of a singular hypersurface proposed by Auroux and demonstrate its desirable properties. In addition, we discuss how this definition can be applied to homological mirror symmetry at various large complex structure limits.