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arXiv · 2601.00544

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

Shunya Adachi·Kazuki Hiroe
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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.

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Shunya Adachi, Kazuki Hiroe. 2026-01-02. On the Riemann-Hilbert problem for hyperplane arrangements with a good line. https://arxiv.org/abs/2601.00544

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