$\Delta_C(t)$, and say that $\Delta_C(t)$ is *non-trivial* if $q(t)\neq 1$.

The most general tool for computing $\Delta_C$ is a formula by Libgober (see [@L1]) that involves type and relative position of the singularities of $C$; one can use it to verify one of the striking features of the Alexander polynomial: that it is rather hard to find curves for which it is non-trivial. This has led researchers to look for classes of curves for which the non-triviality of $\Delta_C$ could be detected by easier means, without the need to directly compute the whole polynomial. Line arrangements, which we will denote by ${\overline{{\mathcal{A}}}}$, are one of these classes. The reason for this choice is two-fold: on the one hand, they are curves with the simplest possible singularities; on the other hand, one may try and take advantage of the combinatorial nature of such objects, encoded in their intersection semilattices $L({\overline{{\mathcal{A}}}})$.

Indeed, over the course of the years many examples and results have shown that the non-triviality of $\Delta_{{\overline{{\mathcal{A}}}}}$ might be detected simply by looking at $L({\overline{{\mathcal{A}}}})$; in order to present them properly, we need to introduce the notion of multinet [@FY; @PS]:

\[defn:multinets\] Let ${\overline{{\mathcal{A}}}}$ be a line arrangement, ${\mathcal{N}}$ denote 