The Coupled Hitchin-He Equations: Integrable Deformations and Rigidity of the Moduli Space
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908783353004032 |
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| author | He, Haoran He, Qichen |
| author_facet | He, Haoran He, Qichen |
| contents | We introduce the \emph{parameter-geometrization} to the Hitchin system, a paradigm embedding deformation parameters into geometry via the coupled Hitchin-He equations on a surface with boundary. A boundary term couples a second Higgs field $ψ$, recovering the classical system at $α=0$. We prove a unique, smooth solution branch exists near $α=0$ (Theorem A). The system is integrable, admitting a Lax pair (Theorem B). Crucially, the moduli space $\mathcal{M}_α$ is analytically isomorphic to $\mathcal{M}_0$ for small $|α|$, preserving the Hitchin fibration -- revealing a deep rigidity where all moduli are controlled by the primary Higgs field (Theorem C). Using the \emph{nonlinear embedding} technique that casts the deformed system into the form of a classical Higgs bundle system, whose integrability and geometry are well-understood, we extends the framework to compact Kähler manifolds (Theorem D). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Coupled Hitchin-He Equations: Integrable Deformations and Rigidity of the Moduli Space He, Haoran He, Qichen Differential Geometry 53C07, 14D21, 35J50, 37K10 We introduce the \emph{parameter-geometrization} to the Hitchin system, a paradigm embedding deformation parameters into geometry via the coupled Hitchin-He equations on a surface with boundary. A boundary term couples a second Higgs field $ψ$, recovering the classical system at $α=0$. We prove a unique, smooth solution branch exists near $α=0$ (Theorem A). The system is integrable, admitting a Lax pair (Theorem B). Crucially, the moduli space $\mathcal{M}_α$ is analytically isomorphic to $\mathcal{M}_0$ for small $|α|$, preserving the Hitchin fibration -- revealing a deep rigidity where all moduli are controlled by the primary Higgs field (Theorem C). Using the \emph{nonlinear embedding} technique that casts the deformed system into the form of a classical Higgs bundle system, whose integrability and geometry are well-understood, we extends the framework to compact Kähler manifolds (Theorem D). |
| title | The Coupled Hitchin-He Equations: Integrable Deformations and Rigidity of the Moduli Space |
| topic | Differential Geometry 53C07, 14D21, 35J50, 37K10 |
| url | https://arxiv.org/abs/2601.16521 |