Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers

Brent Everitt; Paul Turner

doi:10.1007/s00209-022-03106-4

Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers

Brent Everitt, Paul Turner

Mathematics

Research output: Contribution to journal › Article › peer-review

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 [EverittTurner19a], which in turn are 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.

Original language	English
Pages (from-to)	1451-1475
Journal	Mathematische Zeitschrift
Volume	302
Early online date	23 Aug 2022
DOIs	https://doi.org/10.1007/s00209-022-03106-4
Publication status	Published - 23 Aug 2022

Bibliographical note

Access to Document

10.1007/s00209-022-03106-4Licence: CC BY

Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers
© The Author(s) 2022
Final published version, 612 KBLicence: CC BY

https://arxiv.org/abs/1908.04500

Cite this

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