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Perverse sheaves over real hyperplane arrangements. (English) Zbl 1360.14062

Let \(X\) be a smooth complex algebraic variety and \(\mathcal X = (X_{\alpha})\) be a complex algebraic Whitney stratification of \(X\). Fix a base field \(\mathbf k\). One then has the abelian category \(Perv(X;X)\) of \(X\)-smooth perverse sheaves of \(\mathbf k\)-vector spaces on \(X\). Understanding this category is one of the central problems of topology of algebraic varieties. In many applications it is important to have an explicit description of \(Perv(X;X)\) as the category of \(\mathbf k\)-representations of some quiver with relations.
In this paper the authors consider the case when \(X = \mathbf C_n\) and \(X\) is given by an arrangement \(\mathcal H_{\mathbf C}\) of linear hyperplanes in \(X\) with real equations (so \(\mathcal H_{\mathbf C}\) is the complexification of an arrangement \(\mathcal H\) of hyperplanes in \(\mathbf R_n\)). They denote the corresponding category \(Perv(\mathbf C_n; \mathcal H\)) and give a complete, combinatorial description of it.
Reviewer: Cenap Özel (Bolu)

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14N15 Classical problems, Schubert calculus
18E30 Derived categories, triangulated categories (MSC2010)
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References:

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