# Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers

## TL;DR

This paper computes sheaf homology for hyperplane arrangements using Boolean covers and cellular methods, extending previous results and providing new computational tools like a deletion-restriction sequence.

## Contribution

It introduces Boolean covers and cellular homology techniques for sheaf homology of hyperplane arrangements, generalizing earlier work and Lusztig's results.

## Key findings

- Computed sheaf homology with exterior sheaf coefficients.
- Developed cellular homology methods for Boolean covers.
- Established a deletion-restriction long exact sequence.

## Abstract

We compute the sheaf homology of the intersection lattice of a hyperplane arrangement with coefficients in the graded exterior sheaf of the natural sheaf. This builds on the results of our previous paper, where this homology was computed for the natural sheaf, itself a generalisation of an old result of Lusztig. The computational machinery we develop in this paper is quite different though: sheaf homology is lifted to what we call Boolean covers, where we instead compute homology cellularly. A number of tools are given for the cellular homology of these Boolean covers, including a deletion-restriction long exact sequence.