# Perverse Sheaves over Real Hyperplane Arrangements II

### Mikhail Kapranov

University of Tokyo, Kashiwa, Chiba, Japan### Vadim Schechtman

Université Paul Sabatier, Toulouse, France

## Abstract

Let $H$ be an arrangement of hyperplanes in $R_{n}$ and $Perv(CCn,H)$ 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 $E_{A,B}$ labeled 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 $C$. A matrix diagram is formally similar to a datum describing a constructible (nonperverse) sheaf but with the direction of one-half of the arrows reversed.

## Cite this article

Mikhail Kapranov, Vadim Schechtman, Perverse Sheaves over Real Hyperplane Arrangements II. Publ. Res. Inst. Math. Sci. 58 (2022), no. 4, pp. 793–816

DOI 10.4171/PRIMS/58-4-5