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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.19549 |
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| _version_ | 1866929365861793792 |
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| author | Yu, Tony Yue Zhang, Shaowu |
| author_facet | Yu, Tony Yue Zhang, Shaowu |
| contents | We construct the topological Laplace transform functor from Stokes structures of exponential type to constructible sheaves on $\mathbb C$ with vanishing cohomology. We show that it is compatible with the Fourier transform of $D$-modules, and induces an equivalence of categories.
We give two applications of the construction.
First, we study the Fourier transform of B-model nc-Hodge structures associated to Landau-Ginzburg models, and prove the compatibility between the $\mathbb Q$-structure and the Stokes structure from the connection.
Second, we relate the spectral decomposition of nc-Hodge structures to the vanishing cycle decomposition after Fourier transform via choices of Gabrielov paths. This is motivated by the study of the atomic decomposition of A-model nc-Hodge structures associated to smooth projective varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19549 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Laplace Transform and Decomposition of nc-Hodge Structures Yu, Tony Yue Zhang, Shaowu Algebraic Geometry Complex Variables We construct the topological Laplace transform functor from Stokes structures of exponential type to constructible sheaves on $\mathbb C$ with vanishing cohomology. We show that it is compatible with the Fourier transform of $D$-modules, and induces an equivalence of categories. We give two applications of the construction. First, we study the Fourier transform of B-model nc-Hodge structures associated to Landau-Ginzburg models, and prove the compatibility between the $\mathbb Q$-structure and the Stokes structure from the connection. Second, we relate the spectral decomposition of nc-Hodge structures to the vanishing cycle decomposition after Fourier transform via choices of Gabrielov paths. This is motivated by the study of the atomic decomposition of A-model nc-Hodge structures associated to smooth projective varieties. |
| title | Topological Laplace Transform and Decomposition of nc-Hodge Structures |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2405.19549 |