On the Riemann-Hilbert problem for hyperplane arrangements with a good line

Abstract

We study a variant of the Riemann-Hilbert problem on the complements of hyperplane arrangements. This problem asks whether a given local system on the complement can be realized as the solution sheaf of a logarithmic Pfaffian system with constant coefficients. In this paper, we generalize Katz's middle convolution as a functor for local systems on hyperplane complements and show that it preserves the solvability of this problem.