Hitchin fibrations are Ngô fibrations

2025/02/07 by de Cataldo, Mark Andrea, Fringuelli, Roberto, Herrero, Andres Fernandez +1 · 3 citations
#14D20 (Primary) #14D23 #14F20 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.04966

Abstract

We study the geometry of the Hitchin fibration for L-valued G-Higgs bundles over a smooth projective curve of genus g, where G is a reductive group and 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 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.

Cited by

• Stable cohomology of universal character varieties
• Multiplicative dimensional reduction
• Hilbert schemes of elliptic surfaces: group actions and derived categories

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