Hitchin fibration under ramified coverings

Thiago Fassarella; Frank Loray

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arXiv · 2208.10130

Hitchin fibration under ramified coverings

Thiago Fassarella·Frank Loray

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Abstract

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 $\rightarrow$ 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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BibTeX RIS

Thiago Fassarella, Frank Loray. 2023-03-22. Hitchin fibration under ramified coverings. https://arxiv.org/abs/2208.10130

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