Mirror symmetry and Fukaya categories of singular hypersurfaces
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arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866929655028645888 |
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| author | Jeffs, Maxim |
| author_facet | Jeffs, Maxim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_09764 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Mirror symmetry and Fukaya categories of singular hypersurfaces Jeffs, Maxim Symplectic Geometry Algebraic Geometry 53D37 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. |
| title | Mirror symmetry and Fukaya categories of singular hypersurfaces |
| topic | Symplectic Geometry Algebraic Geometry 53D37 |
| url | https://arxiv.org/abs/2012.09764 |