Perverse Sheaves over Real Hyperplane Arrangements II

Abstract

Let H be an arrangement of hyperplanes in R and PervpC,Hq be the category of perverse sheaves on C smooth with respect to the stratification given by complexified flats of H. We give a description of PervpC,Hq in terms of “matrix diagrams”, i.e., diagrams formed by vector spaces EA,B labelled by pairs pA,Bq of real faces of H (of all dimensions) or, equivalently, by the cells iA ` B of a natural cell decomposition of C. 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.