Projective Equivalence of Smooth Hypersurfaces via Cyclic Covers

Abstract

In this paper, we prove that for any smooth hypersurface $Y$ of degree $d$ in ${\mathbb{P}}_k^{n+1}$, the cyclic $d$-fold cover $\tilde{Y}\to {\mathbb{P}}_k^{n+1}$ branched along $Y$ completely characterizes $Y$ up to projective equivalence. This solves a question asked by Huybrechts in [Huy23, §1.5.6].

5 pages