Perverse sheaves over real hyperplane arrangements

Mikhail Kapranov; Vadim Schechtman

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arXiv · 1403.5800

Perverse sheaves over real hyperplane arrangements

Mikhail Kapranov·Vadim Schechtman

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Abstract

Let H be an arrangement of real hyperplanes in R^n. The complexification of H defines a natural stratification of C^n. We denote by Perv(C^n, H) the category of perverse sheaves on C^n smooth with respect to this stratification. We give a description of Perv(C^n, 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.

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Mikhail Kapranov, Vadim Schechtman. 2014-03-23. Perverse sheaves over real hyperplane arrangements. https://arxiv.org/abs/1403.5800

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