Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers

Brent Everitt, Paul Turner

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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 languageEnglish
Pages (from-to)1451-1475
JournalMathematische Zeitschrift
Early online date23 Aug 2022
Publication statusPublished - 23 Aug 2022

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