For every split reductive group G, the Hitchin fibration in the canonical and logarithmic cases is an Ngô fibration, so its direct image splits into Ngô strings.
Equidimensionality of complex Lagrangian fibrations
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We prove that every irreducible component of a fibre of a complex Lagrangian fibration is Lagrangian subvariety. Especially, complex Lagrangian fibations are equidimensional.
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Hitchin fibrations are Ng\^{o} fibrations
For every split reductive group G, the Hitchin fibration in the canonical and logarithmic cases is an Ngô fibration, so its direct image splits into Ngô strings.