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Homological mirror
symmetry for hypersurfaces in $(\mathbb{C}^*)^n$
Mohammed Abouzaid and Denis Auroux |
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Geometry & Topology 28 (2024) 2825–2914
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Abstract |
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We prove a homological mirror symmetry result for maximally degenerating families of hypersurfaces in (B–model) and their mirror toric Landau–Ginzburg A–models. The main technical ingredient of our construction is a “fiberwise wrapped” version of the Fukaya category of a toric Landau–Ginzburg model. With the definition in hand, we construct a fibered admissible Lagrangian submanifold whose fiberwise wrapped Floer cohomology is isomorphic to the ring of regular functions of the hypersurface. It follows that the derived category of coherent sheaves of the hypersurface quasiembeds into the fiberwise wrapped Fukaya category of the mirror. We also discuss an extension to complete intersections. |
Keywords
homological mirror symmetry, Fukaya categories,
Landau–Ginzburg models
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Mathematical Subject Classification
Primary: 53D37
Secondary: 53D40
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References |
Publication
Received: 9 December 2021
Revised: 18 January 2023
Accepted: 17 February 2023
Published: 21 October 2024
Proposed: Richard P Thomas
Seconded: Leonid Polterovich, Yakov Eliashberg
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Authors |
| Mohammed Abouzaid | |
| Department of Mathematics Columbia University New York, NY United States |
Department of Mathematics Stanford University Stanford, CA United States |
| Denis Auroux | |
| Department of Mathematics Harvard University Cambridge, MA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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