Edoukou, Ling and Xing in 2010, conjectured that in \mathbb{ P}^n(\mathbb{ F}_{ q^2}), n \geq 3, the maximum number of common points of a non-degenerate Hermitian variety \mathcal{ 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 \Pi_{ n-2} of codimension 2 such that \Pi_{ n-2} \cap \mathcal{ U}_n is a non-degenerate Hermitian variety. Furthermore, these d hyperplanes are tangent to \mathcal{ 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 \geq 7.
Categories: math.AG