Admissibility of local systems for some classes of line arrangements

Let $\text{A}$ be a line arrangement in the complex projective plane ${\text{PP}}^2$. Denote by $M$ its complement and by $\text{M}$ the set of points in $\text{A}$ with multiplicity at least 3. A rank one local system $\mathcal{L}$ on $M$ is admissible if roughly speaking the dimension of the cohomology groups $H^m(M,\mathcal{L})$ can be computed directly from the cohomology algebra $H^{\ast }(M,\mathbb{C})$. In this work, we give a sufficient condition for the admissibility of all rank one local systems on $M$.