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.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Holomorphic and Operator Theory
Polynomial and algebraic computation
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 2 January 2026
- Document type
- Preprint