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arXiv · 1703.07662

Length and decomposition of the cohomology of the complement to a hyperplane arrangement

Rikard Bøgvad·Iara Gonçalves
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Abstract

Let $\mathcal A$ be a hyperplane arrangement in $\mathbb C^n$. We show that the number of decomposition factors as a perverse sheaf of the direct image $Rj_*\mathbb C_U $ of the constant sheaf on the complement $U$ to the arrangement is given by the Poincar\'e polynomial of the arrangement. Furthermore we describe the composition factors of $Rj_*\mathbb C_U $ as certain local cohomology sheaves and give their multiplicity.

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Rikard Bøgvad, Iara Gonçalves. 2017-03-22. Length and decomposition of the cohomology of the complement to a hyperplane arrangement. https://arxiv.org/abs/1703.07662

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