Projective Equivalence of Smooth Hypersurfaces via Cyclic Covers

2025/08/06 by Li, Zhiyuan, Tang, Zhichao
#14D20 #14J70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.04336

Abstract

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

Citations

• Subgroups of the Projective Linear Group Realized by wild Galois Points
• The Moduli Space of Cubic Threefolds as a Ball Quotient
• The Complex Hyperbolic Geometry of the Moduli Space of Cubic Surfaces

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