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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.06677 |
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| _version_ | 1866910820353441792 |
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| author | Di Gennaro, Roberta Miró-Roig, Rosa Maria |
| author_facet | Di Gennaro, Roberta Miró-Roig, Rosa Maria |
| contents | A hypersurface $X\subset \mathbb P^n$ is said to be free if its associated sheaf $T_X$ of vector fields tangent to $X$ is a free ${\mathcal O}_{\mathbb P^n}$-module. So far few examples of free hypersurfaces are known. In this short note, we reinterpret Saito's criterion of freeness in terms of multiple eigenschemes (ME) and as application we construct huge families of new examples of free reduced hypersurfaces in $\mathbb P^n$. All of them are union of hypersurfaces in a suitable pencil. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Saito's theorem revisited and application to free pencils of hypersurfaces Di Gennaro, Roberta Miró-Roig, Rosa Maria Algebraic Geometry A hypersurface $X\subset \mathbb P^n$ is said to be free if its associated sheaf $T_X$ of vector fields tangent to $X$ is a free ${\mathcal O}_{\mathbb P^n}$-module. So far few examples of free hypersurfaces are known. In this short note, we reinterpret Saito's criterion of freeness in terms of multiple eigenschemes (ME) and as application we construct huge families of new examples of free reduced hypersurfaces in $\mathbb P^n$. All of them are union of hypersurfaces in a suitable pencil. |
| title | Saito's theorem revisited and application to free pencils of hypersurfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.06677 |