Decomposition factors of D-modules on hyperplane configurations in general position

TL;DR

This paper investigates the structure of D-modules associated with hyperplane arrangements, providing explicit decomposition series and criteria for irreducibility based on resolution data.

Contribution

It introduces a method to compute decomposition series of D-modules on hyperplane configurations and offers a criterion for their irreducibility in general position.

Findings

Explicit decomposition series for D-modules on hyperplane arrangements

A sufficient criterion for irreducibility based on resolution data

Application to normal crossings hyperplane configurations

Abstract

We calculate the decomposition series of the D-module defined as the push-forward of a rank one linear system on the complement of a normal crossings hyperplane configuration and use data of a resolution of singularities to give a sufficient criterion of the irreducibility of the corresponding module in general.