Hitchin fibrations are Ngô fibrations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917916251783168 |
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| author | de Cataldo, Mark Andrea Fringuelli, Roberto Herrero, Andres Fernandez Mauri, Mirko |
| author_facet | de Cataldo, Mark Andrea Fringuelli, Roberto Herrero, Andres Fernandez Mauri, Mirko |
| contents | We study the geometry of the Hitchin fibration for $\mathcal{L}$-valued $G$-Higgs bundles over a smooth projective curve of genus $g$, where $G$ is a reductive group and $\mathcal{L}$ is a suitably positive line bundle. We show that the Hitchin fibration admits the structure of a weak Abelian fibration. In the case when the line bundle $\mathcal{L}$ is a twist of the canonical bundle of the curve by a (possibly empty) reduced effective divisor, we prove a cohomological bound and $δ$-regularity of the weak Abelian fibration. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_04966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hitchin fibrations are Ngô fibrations de Cataldo, Mark Andrea Fringuelli, Roberto Herrero, Andres Fernandez Mauri, Mirko Algebraic Geometry 14D20 (Primary), 14D23, 14F20 (Secondary) We study the geometry of the Hitchin fibration for $\mathcal{L}$-valued $G$-Higgs bundles over a smooth projective curve of genus $g$, where $G$ is a reductive group and $\mathcal{L}$ is a suitably positive line bundle. We show that the Hitchin fibration admits the structure of a weak Abelian fibration. In the case when the line bundle $\mathcal{L}$ is a twist of the canonical bundle of the curve by a (possibly empty) reduced effective divisor, we prove a cohomological bound and $δ$-regularity of the weak Abelian fibration. |
| title | Hitchin fibrations are Ngô fibrations |
| topic | Algebraic Geometry 14D20 (Primary), 14D23, 14F20 (Secondary) |
| url | https://arxiv.org/abs/2502.04966 |