Free divisors and duality for D-modules

TL;DR

This paper establishes a duality formula between two D-modules linked to free divisors in complex space, expanding theoretical understanding and providing applications in the study of free divisors and D-modules.

Contribution

It introduces a new duality formula connecting D-modules associated with free divisors, building on prior work and offering novel insights and applications.

Findings

Proves a duality formula for D-modules related to free divisors

Extends the theoretical framework connecting free divisors and D-modules

Provides applications demonstrating the utility of the duality in complex analysis

Abstract

The relationship between ${\cal D}$-modules and free divisors has been studied in a general setting by L. Narv\'aez and F.J. Calder\'on. Using the ideas of these works we prove in this article a duality formula between two ${\cal D}$-modules associated to a class of free divisors on ${\bf C}^n$ and we give some applications