Hyperplane Sections of Hypersurfaces

2020/01/29 by Yiran Cheng, Cheng, Yiran
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2001.10983

openalex publication_date 2020/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute some numerical invariants of the lines on hyperplane sections of a smooth cubic threefold over complex numbers. We also prove that for any smooth hypersurface X⊂ \mathbb Pⁿ⁺¹ of degree d over an algebraically closed field of characteristic zero, if d>n>1 and (n,d)≠ (2,3),(3,4), then a general hyperplane section only admits finitely many others which are isomorphic to it.

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