Maximum number of points of intersection of a non-degenerate Hermitian variety and a cubic hypersurface

2025/04/17 by Subrata Manna, Manna, Subrata
Mathematics · #05B25 #14G15 #4G05 #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.2504.13106

openalex publication_date 2025/04/17 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

Edoukou, Ling and Xing in 2010, conjectured that in ℙⁿ(\mathbbF_q²), n ≥ 3, the maximum number of common points of a non-degenerate Hermitian variety U_n and a hypersurface of degree d is achieved only when the hypersurface is a union of d distinct hyperplanes meeting in a common linear space Π_n-2 of codimension 2 such that Π_n-2 ∩ U_n is a non-degenerate Hermitian variety. Furthermore, these d hyperplanes are tangent to U_n if n is odd and non-tangent if n is even. In this paper, we show that the conjecture is true for d = 3 and q ≥ 7.

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