Mirror symmetry and Fukaya categories of singular hypersurfaces
arXiv:2012.09764 · doi:10.1016/j.aim.2021.108116
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.
v3: 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