Perverse Sheaves over Real Hyperplane Arrangements II

  • Mikhail Kapranov

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

    Université Paul Sabatier, Toulouse, France
Perverse Sheaves over Real Hyperplane Arrangements II cover

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Abstract

Let be an arrangement of hyperplanes in and be the category of perverse sheaves on smooth with respect to the stratification given by complexified flats of . We give a description of in terms of “matrix diagrams”, i.e., diagrams formed by vector spaces labeled by pairs of real faces of (of all dimensions) or, equivalently, by the cells of a natural cell decomposition of . 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