Logarithmic differential operators and logarithmic de Rham complexes relative to a free divisor

Abstract

We prove a structure theorem for the differential operator in the 0-term of the \({\cal V}\)-filtration with respect to a free divisor. Using this theorem, we give a formula for the logarithmic de Rham complex in terms of \({\cal V}_0\)-modules. We also give a sufficient condition for perversity of the logarithmic de Rham complex.