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arXiv · 2012.09764

Mirror symmetry and Fukaya categories of singular hypersurfaces

Maxim Jeffs
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Abstract

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 Kn\"orrer 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.

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Maxim Jeffs. 2020-12-17. Mirror symmetry and Fukaya categories of singular hypersurfaces. https://doi.org/10.1016/j.aim.2021.108116

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