Projective Equivalence of Smooth Hypersurfaces via Cyclic Covers

Published 6 Aug 2025 in math.AG | (2508.04336v1)

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.

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