Mirror symmetry and Fukaya categories of singular hypersurfaces

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 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.

arXiv commentv3: 36 pages, 11 figures; revised from version in Adv. Math. to correct typos, redo figures, update references, improve results; forms part of the author's PhD thesis

References in corpus (8)

• Covariantly functorial wrapped Floer theory on Liouville sectors
• On partially wrapped Fukaya categories
• Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry
• Exact Lagrangian submanifolds in simply-connected cotangent bundles
• Arithmetic mirror symmetry for the 2-torus
• Derived Kn"orrer periodicity and Orlov's theorem for gauged Landau-Ginzburg models
• Mirror symmetry for the Landau-Ginzburg A-model $M={\mathbb{C}}^n,W=z_1\cdots z_n$
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Cited by in corpus (2)

• Mirror symmetry for Berglund-Hübsch Milnor fibers
• Homological mirror symmetry for functors between Fukaya categories of very affine hypersurfaces