D-Modules and arrangements of hyperplanes

Let A be a central arrangement of hyperplanes in Cⁿ defined by the homogeneous polynomial d_A. Let D_n be the Weyl algebra of rank n over C and let [Math equation] be the algebra of rational functions on the variety [math equation]. Studying the structure of P as a D_n-module we obtain a sequence of new D_n-modules. These modules allow us to define useful complexes that determine the De Rham cohomology of [math equation]. Finally we compute the Poincaré series of P.