Fukaya categories of blowups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866912835347415040 |
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| author | Venugopalan, Sushmita Woodward, Chris T. Xu, Guangbo |
| author_facet | Venugopalan, Sushmita Woodward, Chris T. Xu, Guangbo |
| contents | We compute the Fukaya category of the symplectic blowup of a compact rational symplectic manifold at a point in the following sense: Suppose a collection of Lagrangian branes satisfy Abouzaid's criterion for split-generation of a bulk-deformed Fukaya category of cleanly-intersecting Lagrangian branes. We show that for a small blow-up parameter, their inverse images in the blowup together with a collection of branes near the exceptional locus split-generate the Fukaya category of the blowup. This categorifies a result on quantum cohomology by Bayer and is an example of a more general conjectural description of the behavior of the Fukaya category under transitions occuring in the minimal model program, namely that mmp transitions generate additional summands. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_12264 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Fukaya categories of blowups Venugopalan, Sushmita Woodward, Chris T. Xu, Guangbo Symplectic Geometry 53D40 We compute the Fukaya category of the symplectic blowup of a compact rational symplectic manifold at a point in the following sense: Suppose a collection of Lagrangian branes satisfy Abouzaid's criterion for split-generation of a bulk-deformed Fukaya category of cleanly-intersecting Lagrangian branes. We show that for a small blow-up parameter, their inverse images in the blowup together with a collection of branes near the exceptional locus split-generate the Fukaya category of the blowup. This categorifies a result on quantum cohomology by Bayer and is an example of a more general conjectural description of the behavior of the Fukaya category under transitions occuring in the minimal model program, namely that mmp transitions generate additional summands. |
| title | Fukaya categories of blowups |
| topic | Symplectic Geometry 53D40 |
| url | https://arxiv.org/abs/2006.12264 |