This definition from the Clader paper “Moduli theory of \(r\)-braided hyperplane arrangements”.
Definition
A hyperplane arrangement in \(\mathbb P^N\) is a finite collection \[\mathcal A = \{H_1,...,H_k\}\] of hyperplanes in \(\mathbb P^N\). The intersection lattice of \(\mathcal A\) is the collection \(\mathcal L_{\mathcal A}\) of all intersections of elements in \(\mathcal A\); \[\mathcal L_{\mathcal A} = \left\{H_I := \bigcap_{i \in I}H_i ~\middle|I\subset [1..k] ~\right\}.\] We make \(\mathcal L_{\mathcal A}\) a poset under reverse inclusion (for some reason) so that the unique minimal element is \(H_{\emptyset} = \mathbb P^N\). The complement of the arrangement is \(Y^\circ = \mathbb P^N \setminus \bigcup_{i=1}^k H_i\).
We call this arrangement essential if \(\bigcap_{i=1}^k H_i = \emptyset,\) or equivalently, if the corresponding hyperplane arrangement in \(\mathbb A^{N+1} = \Spec (\mathcal O(1))\) the tautological line bundle over \(\mathbb P^N\) has total intersection equal to the origin.