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arXiv · 1910.01677

Perverse sheaves over real hyperplane arrangements II

Mikhail Kapranov·Vadim Schechtman
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Abstract

Let H be an arrangement of hyperplanes in R^n and Perv(C^n,H) be the category of perverse sheaves on C^n smooth with respect to the stratification given by complexified flats of H. We give a description of Perv(C^n,H) in terms of "matrix diagrams", i.e., diagrams formed by vector spaces E_{AB} labelled by pairs A,B of real faces of H (of all dimensions) or, equivalently, by the cells iA+B of a natural cell decomposition of C^n. A matrix diagram is formally similar to a datum describing a constructible (non-perverse) sheaf but with the direction of one half of the arrows reversed.

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Mikhail Kapranov, Vadim Schechtman. 2019-10-03. Perverse sheaves over real hyperplane arrangements II. https://arxiv.org/abs/1910.01677

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