Projective Equivalence of Smooth Hypersurfaces via Cyclic Covers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914113262714880 |
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| author | Li, Zhiyuan Tang, Zhichao |
| author_facet | Li, Zhiyuan Tang, Zhichao |
| contents | In this paper, we prove that for any smooth hypersurface $Y$ of degree $d$ in $\mathbb{P}^{n+1}_k$, the cyclic $d$-fold cover $\widetilde{Y} \to \mathbb{P}^{n+1}_k$ branched along $Y$ completely characterizes $Y$ up to projective equivalence. This solves a question asked by Huybrechts in [Huy23, §1.5.6]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Projective Equivalence of Smooth Hypersurfaces via Cyclic Covers Li, Zhiyuan Tang, Zhichao Algebraic Geometry 14J70, 14D20 In this paper, we prove that for any smooth hypersurface $Y$ of degree $d$ in $\mathbb{P}^{n+1}_k$, the cyclic $d$-fold cover $\widetilde{Y} \to \mathbb{P}^{n+1}_k$ branched along $Y$ completely characterizes $Y$ up to projective equivalence. This solves a question asked by Huybrechts in [Huy23, §1.5.6]. |
| title | Projective Equivalence of Smooth Hypersurfaces via Cyclic Covers |
| topic | Algebraic Geometry 14J70, 14D20 |
| url | https://arxiv.org/abs/2508.04336 |