Kodaira-Spencer Map on the Hitchin-Simpson Correspondence
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914162976751616 |
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| author | Hu, Tianzhi Shi, Mai Sun, Ruiran Zuo, Kang |
| author_facet | Hu, Tianzhi Shi, Mai Sun, Ruiran Zuo, Kang |
| contents | We define the isomonodromic deformation of a Higgs bundle over a compact Riemann surface via the Hitchin-Simpson correspondence and the isomonodromic deformation of a local system. This deformation defines a real analytic section of the relative Dolbeault moduli space, yielding a real analytic foliation on this moduli. This foliation generalizes the Betti foliation defined by the Betti map in the study of abelian schemes. We provide a precise form for the holomorphic and anti-holomorphic derivatives of the isomonodromic deformation of a Higgs bundle. Subsequently, we extend the classical non-abelian Kodaira-Spencer map using the anti-holomorphic derivative. Additionally, we prove that if the isomonodromic deformation of a graded Higgs bundle is not holomorphic, then the isomonodromically deformed Higgs field is non-nilpotent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14272 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kodaira-Spencer Map on the Hitchin-Simpson Correspondence Hu, Tianzhi Shi, Mai Sun, Ruiran Zuo, Kang Algebraic Geometry We define the isomonodromic deformation of a Higgs bundle over a compact Riemann surface via the Hitchin-Simpson correspondence and the isomonodromic deformation of a local system. This deformation defines a real analytic section of the relative Dolbeault moduli space, yielding a real analytic foliation on this moduli. This foliation generalizes the Betti foliation defined by the Betti map in the study of abelian schemes. We provide a precise form for the holomorphic and anti-holomorphic derivatives of the isomonodromic deformation of a Higgs bundle. Subsequently, we extend the classical non-abelian Kodaira-Spencer map using the anti-holomorphic derivative. Additionally, we prove that if the isomonodromic deformation of a graded Higgs bundle is not holomorphic, then the isomonodromically deformed Higgs field is non-nilpotent. |
| title | Kodaira-Spencer Map on the Hitchin-Simpson Correspondence |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2511.14272 |