Locally quasi-homogeneous free divisors are Koszul free

Abstract

Let X be a complex analytic manifold and D ⊂ X be a free divisor. If D is locally quasi-homogeneous, then the logarithmic de Rham complex associated to D is quasi-isomorphic to Rj∗(CX\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.