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arXiv · 2508.04336

Projective Equivalence of Smooth Hypersurfaces via Cyclic Covers

Zhiyuan Li·Zhichao Tang
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Abstract

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, \S 1.5.6].

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Zhiyuan Li, Zhichao Tang. 2025-08-06. Projective Equivalence of Smooth Hypersurfaces via Cyclic Covers. https://arxiv.org/abs/2508.04336

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