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