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arXiv · 2502.04966

Hitchin fibrations are Ng\^{o} fibrations

Mark Andrea de Cataldo·Roberto Fringuelli·Andres Fernandez Herrero·Mirko Mauri
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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.

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Mark Andrea de Cataldo, Roberto Fringuelli, Andres Fernandez Herrero, Mirko Mauri. 2025-02-07. Hitchin fibrations are Ng\^{o} fibrations. https://arxiv.org/abs/2502.04966

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