Author:
Everitt Brent,Turner Paul
Abstract
AbstractWe compute the sheaf homology of the intersection lattice of a hyperplane arrangement with coefficients in the graded exterior sheaf $$\varLambda ^\bullet F$$
Λ
∙
F
of the natural sheaf F. This builds on the results of our previous paper Everitt and Turner (Adv Math 402:Paper No. 108354, 2022. https://doi.org/10.1016/j.aim.2022.108354) where this homology was computed for $$\varLambda ^1F=F$$
Λ
1
F
=
F
, 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.
Publisher
Springer Science and Business Media LLC
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