Characterization of non-singular hyperplanes of $H(s,q^2)$ in $\mathrm{P}\mathrm{G}(s,q^2)$

In this paper, we present a combinatorial characterization of the hyperplanes associated with non-singular hermitian varieties $H(s,q^2)$ in the projective space $\mathrm{P}\mathrm{G}(s,q^2)$ where $s\ge 3$ and $q>2$. By analyzing the intersection numbers of hyperplanes with points and co-dimension $2$ subspaces, we establish necessary and sufficient conditions for a hyperplane to be part of the hermitian variety. This approach extends previous characterizations of hermitian varieties based on intersection properties, providing a purely combinatorial method for identifying their hyperplanes.