Resonance webs of hyperplane arrangements

TL;DR

This paper introduces the concept of resonance webs derived from hyperplane arrangements and explores their properties, focusing on the structure of their abelian relations.

Contribution

It initiates the study of resonance webs associated with hyperplane arrangements, emphasizing their abelian relation spaces and geometric structures.

Findings

Resonance webs are constructed from hyperplane arrangements via associated foliations.

The paper analyzes the space of abelian relations of these webs.

Foundations for further geometric and algebraic study of resonance webs are established.

Abstract

Each irreducible component of the first resonance variety of a hyperplane arrangement naturally determines a codimension one foliation on the ambient space. The superposition of these foliations define what we call the resonance web of the arrangement. In this paper we initiate the study of these objects with emphasis on their spaces of abelian relations.