Vanishing results for the Aomoto complex of real hyperplane arrangements via minimality

TL;DR

This paper establishes vanishing results for the cohomology of the Aomoto complex associated with real hyperplane arrangements, using minimality and chamber descriptions, and offers a new proof for existing local system cohomology vanishing theorems.

Contribution

It introduces a novel approach leveraging minimal arrangements and chamber descriptions to prove vanishing results for the Aomoto complex and local system cohomology.

Findings

Proves vanishing of Aomoto complex cohomology over any coefficient ring.

Provides a new proof for the vanishing theorem of local system cohomology.

Uses minimality and chamber descriptions to achieve these results.

Abstract

We prove vanishing results of the cohomology groups of Aomoto complex over arbitrary coefficient ring for real hyperplane arrangements. The proof is using minimality of arrangements and descriptions of Aomoto complex in terms of chambers. Our methods also provide a new proof for the vanishing theorem of local system cohomology groups which was first proved by Cohen, Dimca and Orlik.