Triangular isomonodromic solutions to a Fuchsian system from superelliptic curves
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910106243825664 |
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| author | Ghabra, Anwar Al Piché, Benjamin Shramchenko, Vasilisa |
| author_facet | Ghabra, Anwar Al Piché, Benjamin Shramchenko, Vasilisa |
| contents | We give fundamental solutions of arbitrarily sized matrix Fuchsian linear systems, in the case where the coefficients $B^{(i)}$ of the systems are matrix solutions of the Schlesinger system that are upper triangular, and whose eigenvalues follow an arithmetic progression of a rational difference. The values on the superdiagonals of the matrices $B^{(i)}$ are given by contour integrals of meromorphic differentials defined on Riemann surfaces obtained by compactification of superelliptic curves. We show that our fundamental solutions are isomonodromic by obtaining their monodromy matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Triangular isomonodromic solutions to a Fuchsian system from superelliptic curves Ghabra, Anwar Al Piché, Benjamin Shramchenko, Vasilisa Mathematical Physics We give fundamental solutions of arbitrarily sized matrix Fuchsian linear systems, in the case where the coefficients $B^{(i)}$ of the systems are matrix solutions of the Schlesinger system that are upper triangular, and whose eigenvalues follow an arithmetic progression of a rational difference. The values on the superdiagonals of the matrices $B^{(i)}$ are given by contour integrals of meromorphic differentials defined on Riemann surfaces obtained by compactification of superelliptic curves. We show that our fundamental solutions are isomonodromic by obtaining their monodromy matrices. |
| title | Triangular isomonodromic solutions to a Fuchsian system from superelliptic curves |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2507.10692 |