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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.04382 |
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| _version_ | 1866909808167223296 |
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| author | Hiatt, Scott |
| author_facet | Hiatt, Scott |
| contents | Let $X$ be a complex algebraic variety. With $\mathbb{Q}$-coefficients, the compactly supported cohomology groups $H^{i}_{c}(X, \mathbb{Q})$ and the compactly supported intersection cohomology groups $IH^{i}_{c}(X, \mathbb{Q})$ have mixed Hodge structures. We compare these two mixed Hodge structures for varieties with pre-$k$-rational singularities. We then study various notions of differential forms on varieties with pre-$k$-rational singularities. In particular, we investigate the depth of the complex $\underlineΩ^{p}_{X}$, where $\underlineΩ^{p}_{X}$ is the $p^{th}$-graded piece of the Du Bois complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differential forms on varieties with pre-$k$-rational singularities Hiatt, Scott Algebraic Geometry Let $X$ be a complex algebraic variety. With $\mathbb{Q}$-coefficients, the compactly supported cohomology groups $H^{i}_{c}(X, \mathbb{Q})$ and the compactly supported intersection cohomology groups $IH^{i}_{c}(X, \mathbb{Q})$ have mixed Hodge structures. We compare these two mixed Hodge structures for varieties with pre-$k$-rational singularities. We then study various notions of differential forms on varieties with pre-$k$-rational singularities. In particular, we investigate the depth of the complex $\underlineΩ^{p}_{X}$, where $\underlineΩ^{p}_{X}$ is the $p^{th}$-graded piece of the Du Bois complex. |
| title | Differential forms on varieties with pre-$k$-rational singularities |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.04382 |