Local duality and mixed Hodge modules

TL;DR

This paper explores the relationship between filtered holonomic D-modules, their duals, and characteristic varieties within the context of polarized Hodge modules on smooth algebraic varieties, using Saito's Cohen-Macaulay result and local duality.

Contribution

It establishes a new connection between graded quotients, sheaf-theoretic duals, and characteristic varieties for polarized Hodge modules, advancing the understanding of their structure.

Findings

Proves a relationship between graded quotients and duals in Hodge modules

Utilizes Saito's Cohen-Macaulay result for the associated graded module

Employs local duality on the cotangent bundle

Abstract

We establish a relationship between the graded quotients of a filtered holonomic D-module, their sheaf-theoretic duals, and the characteristic variety, in case the filtered D-module underlies a polarized Hodge module on a smooth algebraic variety. The proof is based on Saito's result that the associated graded module is Cohen-Macaulay, and on local duality on the cotangent bundle.