Restrictions of mixed Hodge modules using generalized V-filtrations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917539029712896 |
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| author | Chen, Qianyu Dirks, Bradley Olano, Sebastian |
| author_facet | Chen, Qianyu Dirks, Bradley Olano, Sebastian |
| contents | We study generalized $V$-filtrations, defined by Sabbah, on $\mathcal D$-modules underlying mixed Hodge modules on $X\times \mathbf A^r$. Using cyclic covers, we compare these filtrations to the usual $V$-filtration, which is better understood. The main result shows that these filtrations can be used to compute the restriction functors $σ^!, σ^*$, where $σ\colon X \times \{0\} \to X \times \mathbf A^r$ is the inclusion of the zero section.
As an application, we use the restriction result to study singularities of complete intersection subvarieties. These filtrations can be used to study the local cohomology mixed Hodge module. In particular, we classify when weighted homogeneous isolated complete intersection singularities in $\mathbf A^n$ are $k$-Du Bois and $k$-rational. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restrictions of mixed Hodge modules using generalized V-filtrations Chen, Qianyu Dirks, Bradley Olano, Sebastian Algebraic Geometry 14F10, 14B05, 14J17 We study generalized $V$-filtrations, defined by Sabbah, on $\mathcal D$-modules underlying mixed Hodge modules on $X\times \mathbf A^r$. Using cyclic covers, we compare these filtrations to the usual $V$-filtration, which is better understood. The main result shows that these filtrations can be used to compute the restriction functors $σ^!, σ^*$, where $σ\colon X \times \{0\} \to X \times \mathbf A^r$ is the inclusion of the zero section. As an application, we use the restriction result to study singularities of complete intersection subvarieties. These filtrations can be used to study the local cohomology mixed Hodge module. In particular, we classify when weighted homogeneous isolated complete intersection singularities in $\mathbf A^n$ are $k$-Du Bois and $k$-rational. |
| title | Restrictions of mixed Hodge modules using generalized V-filtrations |
| topic | Algebraic Geometry 14F10, 14B05, 14J17 |
| url | https://arxiv.org/abs/2410.09959 |