Locally Quasi-Homogeneous Free Divisors Are Koszul Free

Let $X$ be a complex analytic manifold and $D\subset X$ be a free divisor. If $D$ is locally quasi-homogeneous, then the logarithmic de Rham complex associated to $D$ is quasi-isomorphic to $\mathbf R j_\ast (\mathbb C_{X\setminus D})$, which is a perverse sheaf. On the other hand, the logarithmic de Rham complex associated to a Koszul-free divisor is perverse. In this paper, we prove that every locally quasi-homogeneous free divisor is Koszul free.