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

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 Π{n-2} of codimension 2 such that Π{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.