Perverse sheaves (or D-modules) on vector spaces, constructible with respect to a hyperplane arrangement Let $V$ be a finite dimensional complex vector space and let $\mathcal{A}$ be a finite collection of hyperplanes in $V$. Stratify $V$ by the intersections of elements of $\mathcal{A}$, and consider the category of perverse sheaves on $V$ (or, if you prefer, regular holonomic D-modules) that are constructible with respect to this stratification. I am interested in learning how to explicitly identify this category with a certain category of representations of a quiver. I have in mind the following example, having already understood the stratification of the one dimensional vector space $\mathbb{C}$ arising from one hyperplane $\\{ 0 \\}$: let $V=\mathbb{C}^2$ with hyperplanes $$x=0, \quad y=0, \quad x+y=0.$$ I know the definitions of vanishing and nearby cycles already, and I'd appreciate expert help doing these explicit calculations!

Have a look at this Kapranov's and Schechtman's paper called "Perverse sheaves over real hyperplane arrangements", that you can find on arxiv here :

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It may interest you.