Volume 229 (2022)
Mirror symmetry for very affine hypersurfaces
Pages: 287 – 346
We show that the category of coherent sheaves on the toric boundary divisor of a smooth quasi-projective toric DM stack is equivalent to the wrapped Fukaya category of a hypersurface in $(C^\times)^n$. Hypersurfaces with every Newton polytope can be obtained. Our proof has the following ingredients. Using recent results on localization, we may trade wrapped Fukaya categories for microlocal sheaf theory along the skeleton of the hypersurface. Using Mikhalkin–Viro patchworking, we identify the skeleton of the hypersurface with the boundary of the Fang–Liu–Treumann–Zaslow skeleton. By proving a new functoriality result for Bondal’s coherent-constructible correspondence, we reduce the sheaf calculation to Kuwagaki’s recent theorem on mirror symmetry for toric varieties.
Received 26 October 2018
Received revised 20 January 2021
Accepted 2 February 2022
Published 21 February 2023