The Fukaya–Seidel and categorical intersection complex correspondence for hyperplane arrangements

Let $X=(\mathbb{C}^*)^n\subset\mathbb{C}^{n+1}$. A normal crossings divisor in $\mathbb{P}^n$ is the union of $n+1$ hyperplanes in general position. The categorical intersection complex is the complex of categories obtained from the various intersections of these hyperplanes and their push-forward functors. An iterated Lefschetz fibration on $X$ determines a Fukaya–Seidel complex, denoted $\operatorname{FS}(\pi_{\bullet})$. The Fukaya–Seidel and categorical intersection complex correspondence. There exists a family of iterated Lefschetz fibrations $\pi_{\bullet}$ on $X$ such that the corresponding Fukaya–Seidel complex $\operatorname{FS}(\pi_{\bullet})$ is equivalent to the right adjoint of the categorical intersection complex of the normal crossings divisor given by $n+1$ hyperplanes in $\mathbb{P}^n$ in general position. This generalizes the displayed comparison for three lines in $\mathbb{P}^2$; the source does not establish the asserted equivalence or provide evidence resolving the conjecture.