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Pré-Publication, Document De Travail Année : 2022

Hitchin fibration under ramified coverings

Résumé

We are interested in studying the variation of the Hitchin fibration in moduli spaces of parabolic Higgs bundles, under the action of a ramified covering. Given a degree two map π : Y → X between compact Riemann surfaces, we may pull back a Higgs bundle from X to Y , the lifted Higgs bundle tends to have many apparent singularities, then we perform a suitable birational transformation in order to eliminate them. This correspondence preserves the Hitchin fibrations and then its restriction to a general fiber gives a map between Abelian varieties. The aim of this paper is to describe this map.
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Dates et versions

hal-03754844 , version 1 (20-08-2022)
hal-03754844 , version 2 (21-03-2023)

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Thiago Fassarella, Frank Loray. Hitchin fibration under ramified coverings. 2022. ⟨hal-03754844v1⟩
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