Local duality and polarized hodge modules

We nd a relationship between the graded quotients of a ltered holonomic D-module, their duals as coherent sheaves, and the characteristic variety, in case the ltered D-module underlies a polarized Hodge module on a smooth algebraic variety. The proof is based on M. Saito's result that the associated graded module is Cohen-Macaulay, and on local duality for the cotangent bundle. The result plays a role in the study of Ne ́ron models for families of intermediate Jacobians, recently constructed by the author.