Resonance webs of hyperplane arrangements

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.Comment: (v2) Minor changes following suggestions of the referee. To appear in the Proceedings of the 2nd MSJ-SI on Arrangements of Hyperplane