Motivic principal value integrals for hyperplane arrangements

TL;DR

This paper proves a stronger version of a conjecture linking motivic principal value integrals and cohomology support loci specifically for hyperplane arrangements.

Contribution

It provides a new, more robust proof of the conjecture for hyperplane arrangements, advancing understanding in motivic integration and local system cohomology.

Findings

Confirmed the conjecture for hyperplane arrangements

Established a stronger positive result than previously known

Enhanced the connection between motivic integrals and cohomology support loci

Abstract

A conjecture of Denef-Jacobs-Veys relates motivic principal value integrals of multivalued rational top-forms with cohomology support loci of rank one local systems. We give a stronger positive answer to this conjecture for hyperplane arrangements.