Local Duality and Polarized Hodge Modules

Abstract

We establish a relationship between the graded quotients of a filtered holonomic $\mathcal{D}$-module, their duals as coherent sheaves, and the characteristic variety, in case the filtered $\mathcal{D}$-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 Néron models for families of intermediate Jacobians, recently constructed by the author.