Non-existence of holomorphic isomonodromic deformation of a Higgs bundle
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908743079297024 |
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| author | Hu, Tianzhi Sun, Ruiran Zuo, Kang |
| author_facet | Hu, Tianzhi Sun, Ruiran Zuo, Kang |
| contents | We use the cohomological interpretation of anti-holomorphic derivatives of the isomonodromic deformation of a Higgs bundle, as established in our previous work \cite{HSZ}, to provide a short new proof of the non-existence of holomorphic isomonodromic deformation of a generic $\SL$-Higgs bundle and of any non-unitary rank 2 Higgs bundle over the Teichmüller space $\mathcal T_g$, which were previously proved in \cite{biswas}. We also prove the non-existence of holomorphic isomonodromic deformation of any non-unitary rank 3 Higgs bundle over the Teichmüller space $\mathcal T_g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15478 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-existence of holomorphic isomonodromic deformation of a Higgs bundle Hu, Tianzhi Sun, Ruiran Zuo, Kang Algebraic Geometry We use the cohomological interpretation of anti-holomorphic derivatives of the isomonodromic deformation of a Higgs bundle, as established in our previous work \cite{HSZ}, to provide a short new proof of the non-existence of holomorphic isomonodromic deformation of a generic $\SL$-Higgs bundle and of any non-unitary rank 2 Higgs bundle over the Teichmüller space $\mathcal T_g$, which were previously proved in \cite{biswas}. We also prove the non-existence of holomorphic isomonodromic deformation of any non-unitary rank 3 Higgs bundle over the Teichmüller space $\mathcal T_g$. |
| title | Non-existence of holomorphic isomonodromic deformation of a Higgs bundle |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.15478 |