On the Riemann-Hilbert problem for hyperplane arrangements with a good line
Algebraic Geometry
2026-05-29 v3 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2601.00544,
title = {On the Riemann-Hilbert problem for hyperplane arrangements with a good line},
author = {Shunya Adachi and Kazuki Hiroe},
journal= {arXiv preprint arXiv:2601.00544},
year = {2026}
}
Comments
31 pages, a minor correction has been made