Perverse sheaves over real hyperplane arrangements

By M. Kapranov, V. Schechtman. 2014

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Let H be an arrangement of real hyperplanes in R. The complexification of H defines a natural stratification of C. We denote by Perv(C,H) the category of perverse sheaves on C smooth with respect to this stratification. We give a description of Perv(C,H) as the category of representations of an explicit quiver with relations, whose vertices correspond to real faces of H (of all dimensions). The relations are of monomial nature: they identify some pairs of paths in the quiver. They can be formulated in terms of the oriented matroid associated to H.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

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