On the Riemann-Hilbert problem for hyperplane arrangements with a good line
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910268110405632 |
|---|---|
| author | Adachi, Shunya Hiroe, Kazuki |
| author_facet | Adachi, Shunya Hiroe, Kazuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00544 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Riemann-Hilbert problem for hyperplane arrangements with a good line Adachi, Shunya Hiroe, Kazuki Algebraic Geometry Classical Analysis and ODEs 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. |
| title | On the Riemann-Hilbert problem for hyperplane arrangements with a good line |
| topic | Algebraic Geometry Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2601.00544 |