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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/2504.19006 |
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| _version_ | 1866915261787930624 |
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| author | Church, Benjamin |
| author_facet | Church, Benjamin |
| contents | In this note, we prove -- in dimension at most 4 -- a conjectue of Hao which says that a morphism $f : X \to A$ to a simple abelian variety $A$ is smooth if and only if there is a 1-form pulled back from A without any zeros. We also give a complete classification of 4-folds with a 1-form without zeros not admitting a map to an elliptic curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nowhere vanishing 1-forms on 4-folds Church, Benjamin Algebraic Geometry In this note, we prove -- in dimension at most 4 -- a conjectue of Hao which says that a morphism $f : X \to A$ to a simple abelian variety $A$ is smooth if and only if there is a 1-form pulled back from A without any zeros. We also give a complete classification of 4-folds with a 1-form without zeros not admitting a map to an elliptic curve. |
| title | Nowhere vanishing 1-forms on 4-folds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.19006 |