For an essential hyperplane arrangement, the sheaf homology of its intersection lattice with coefficients in the exterior powers of the natural sheaf is concentrated on one diagonal, with dimensions given by derivatives of the characteristic polynomial at 1.
Deletion-restriction for sheaf homology of graded atomic lattices
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We give a long exact sequence for the homology of a graded atomic lattice equipped with a sheaf of modules, in terms of the deleted and restricted lattices. This is then used to compute the homology of the arrangement lattice of a hyperplane arrangement equipped with the natural sheaf. This generalises an old result of Lusztig.
fields
math.AT 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers
For an essential hyperplane arrangement, the sheaf homology of its intersection lattice with coefficients in the exterior powers of the natural sheaf is concentrated on one diagonal, with dimensions given by derivatives of the characteristic polynomial at 1.