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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!

Stephen
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    It really is spelled "constructible". – Stephen Jun 04 '13 at 16:12
  • Also, I know that "representations of a quiver" is somehow too much to hope for---the big stratum in my example has a somewhat complicated fundamental group (seems to be the pure braid group on three strands). The point is that I'd like a concrete description via gluing. – Stephen Jun 04 '13 at 23:05
  • Have a look at this Kapranov's paper. – Olórin Mar 05 '15 at 02:23
  • @user10000100_u Excellent! Thanks very much. If you like, you can convert you comment into an answer that I'll happily accept (the paper is exactly an answer to my question). – Stephen Mar 20 '15 at 16:07
  • Done ;-) Nothing new in it – Olórin Mar 20 '15 at 17:41
  • Actually, I didn't see from mobile, but I already posted this very same answer, which was converted automatically to a comment. Apparently, folks here won't let you decide if you like an answer or not, they'll decide for you. – Olórin Mar 20 '15 at 17:59

1 Answers1

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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 :

http://arxiv.org/pdf/1403.5800.pdf

It may interest you.

Olórin
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