Maximum number of points on an intersection of a cubic threefold and a non-degenerate Hermitian threefold

2024/06/11 by Mrinmoy Datta, Datta, Mrinmoy, Subrata Manna +1
Mathematics · #05B25 #14G05 #14G15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2406.07326

openalex publication_date 2024/06/11 · openalex created_date 2024/06/13 · openalex updated_date 2026/07/28

Abstract

It was conjectured by Edoukou in 2008 that a non-degenerate Hermitian threefold in ℙ⁴ (\mathbbF_q²) has at most d(q⁵+q²) + q³ + 1 points in common with a threefold of degree d defined over \mathbbF_q². He proved the conjecture for d=2. In this paper, we show that the conjecture is true for d = 3 and q ≥ 7.

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