Higher resonance varieties of matroids

TL;DR

This paper explores the resonance varieties of matroids and hyperplane arrangements, revealing new phenomena that emerge when analyzing all cohomological degrees collectively, beyond the traditional focus on degree 1.

Contribution

It introduces new insights into resonance varieties by examining all degrees simultaneously, extending beyond prior degree 1 focus.

Findings

New phenomena in resonance varieties across all degrees

Broader understanding of hyperplane arrangements

Enhanced analysis of matroid cohomology

Abstract

We present some new results about the resonance varieties of matroids and hyperplane arrangements. Though these have been the objects of ongoing study, most work so far has focussed on cohomological degree 1. We show that certain phenomena become apparent only by considering all degrees at once.