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arXiv · 2406.07326

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

Mrinmoy Datta·Subrata Manna
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Abstract

It was conjectured by Edoukou in 2008 that a non-degenerate Hermitian threefold in $\mathbb{P}^4 (\mathbb{F}_{q^2})$ has at most $d(q^5+q^2) + q^3 + 1$ points in common with a threefold of degree $d$ defined over $\mathbb{F}_{q^2}$. He proved the conjecture for $d=2$. In this paper, we show that the conjecture is true for $d = 3$ and $q \ge 7$.

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Mrinmoy Datta, Subrata Manna. 2024-06-11. Maximum number of points on an intersection of a cubic threefold and a non-degenerate Hermitian threefold. https://arxiv.org/abs/2406.07326

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