At the moment, I am reading the paper "on the connectivity of the realization spaces of line arrangements" of Nazir and Yoshinaga.

I would like to extend their Lemma 3.2 to higher dimension. However, I need to better understand the notion of hyperplane generic to a given arrangement.

**Question 1:** Let $\mathcal{A}=\{H_{1},\ldots,H_{m}\}$ be a hyperplane arrangement in $\mathbb{CP}^{d}$ and let $K$ be a hyperplane of $\mathbb{CP}^{d}$. What does it mean that $K$ is *generic* with respect to $\mathcal{A}$?

**Question 2:** For $d=2$ (the case of line arrangements) this notion is equivalent to say that $\det(H_{i},H_{j},K)\neq0$ for $1\leq i<j\leq m$ (here we are assuming that the lines of $\mathcal{A}$ are pairwise distinct). How can we generalize this characterization to higher dimension?