Decomposition of D-modules over a hyperplane arrangement in the plane

TL;DR

This paper analyzes the structure of a specific D-module associated with a plane hyperplane arrangement, providing a detailed algebraic decomposition using Weyl algebra calculations.

Contribution

It introduces a method to explicitly decompose D-modules over plane hyperplane arrangements using algebraic techniques in the Weyl algebra.

Findings

Decomposition series of the D-module is explicitly computed.

Algebraic calculations in the Weyl algebra are effective for analyzing such modules.

Provides new insights into the structure of D-modules over hyperplane arrangements.

Abstract

We consider the D-module defined as the push-forward of a rank one linear system on the complement of a central plane hyperplane arrangement, and calculate its decomposition series, using algebraic calculations in the Weyl algebra.