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Article overview
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Mirror symmetry for very affine hypersurfaces | | Benjamin Gammage
; Vivek Shende
; | | Date: |
10 Jul 2017 | | Abstract: | We show that the category of coherent sheaves on the toric boundary divisor
of a smooth quasiprojective DM toric stack is equivalent to the wrapped Fukaya
category of a hypersurface in a complex torus. Hypersurfaces with every Newton
polytope can be obtained.
Our proof has the following ingredients. Using Mikhalkin-Viro patchworking,
we compute the skeleton of the hypersurface. The result matches the [FLTZ]
skeleton, and in particular is a conical Lagrangian. We invoke the localization
of [GPS1, GPS2] to trade wrapped Fukaya categories for microlocal sheaf theory.
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. | | Source: | arXiv, 1707.2959 | | Services: | Forum | Review | PDF | Favorites | |
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