1. Hitchin fibrations are Ng\^{o} fibrations
- Author
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de Cataldo, Mark Andrea, Fringuelli, Roberto, Herrero, Andres Fernandez, and Mauri, Mirko
- Subjects
Mathematics - Algebraic Geometry ,14D20 (Primary), 14D23, 14F20 (Secondary) - Abstract
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 $\delta$-regularity of the weak Abelian fibration., Comment: 98 pages, comments are welcome
- Published
- 2025