Deformation quantization and perverse sheaves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917766787760128 |
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| author | Gunningham, Sam Safronov, Pavel |
| author_facet | Gunningham, Sam Safronov, Pavel |
| contents | Kashiwara, Polesello, Schapira and D'Agnolo defined canonical deformation quantizations of a holomorphic symplectic manifold and a holomorphic Lagrangian submanifold equipped with an orientation data. The goal of this paper is to use deformation quantization modules to construct a Fukaya-like category of holomorphic Lagrangians, resolving a conjecture of Joyce. Our main result describes the RHom complex between two such deformation quantization modules associated to a pair of Lagrangian submanifolds in terms of the derived geometry of the Lagrangian intersection. Namely, we identify the RHom complex with the DT sheaf associated to the d-critical structure on the Lagrangian intersection. Via a Riemann-Hilbert correspondence this describes the RHom complex in the category of microsheaves of sheaf quantizations of conic holomorphic Lagrangians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07595 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deformation quantization and perverse sheaves Gunningham, Sam Safronov, Pavel Algebraic Geometry Symplectic Geometry Kashiwara, Polesello, Schapira and D'Agnolo defined canonical deformation quantizations of a holomorphic symplectic manifold and a holomorphic Lagrangian submanifold equipped with an orientation data. The goal of this paper is to use deformation quantization modules to construct a Fukaya-like category of holomorphic Lagrangians, resolving a conjecture of Joyce. Our main result describes the RHom complex between two such deformation quantization modules associated to a pair of Lagrangian submanifolds in terms of the derived geometry of the Lagrangian intersection. Namely, we identify the RHom complex with the DT sheaf associated to the d-critical structure on the Lagrangian intersection. Via a Riemann-Hilbert correspondence this describes the RHom complex in the category of microsheaves of sheaf quantizations of conic holomorphic Lagrangians. |
| title | Deformation quantization and perverse sheaves |
| topic | Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2312.07595 |