Fourier transform and Radon transform for mixed Hodge modules
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916265175547904 |
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| author | Dirks, Bradley |
| author_facet | Dirks, Bradley |
| contents | We give a generalization to bi-filtered $\mathcal D$-modules underlying mixed Hodge modules of the relation between microlocalization along $f_1,...,f_r \in \mathcal O_X(X)$ and vanishing cycles along $g = \sum_{i=1}^r y_i f_i$. This leads to an interesting isomorphism between localization triangles. As an application, we use these results to compare the $k$-plane Radon transform and the Fourier-Laplace transform for mixed Hodge modules. This is then applied to the Hodge module structure of certain GKZ systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourier transform and Radon transform for mixed Hodge modules Dirks, Bradley Algebraic Geometry 32C38 We give a generalization to bi-filtered $\mathcal D$-modules underlying mixed Hodge modules of the relation between microlocalization along $f_1,...,f_r \in \mathcal O_X(X)$ and vanishing cycles along $g = \sum_{i=1}^r y_i f_i$. This leads to an interesting isomorphism between localization triangles. As an application, we use these results to compare the $k$-plane Radon transform and the Fourier-Laplace transform for mixed Hodge modules. This is then applied to the Hodge module structure of certain GKZ systems. |
| title | Fourier transform and Radon transform for mixed Hodge modules |
| topic | Algebraic Geometry 32C38 |
| url | https://arxiv.org/abs/2405.19127 |