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Article Dans Une Revue Geometriae Dedicata Année : 2019

Very stable bundles and properness of the Hitchin map

Résumé

Let $X$ be a smooth complex projective curve of genus $g\geq 2$ and let $K$ be its canonical bundle. In this note we show that a stable vector bundle $E$ on $X$ is very stable, i.e. $E$ has no non-zero nilpotent Higgs field, if and only if the restriction of the Hitchin map to the vector space of Higgs fields $H^0(X, \mathrm{End}(E) \otimes K)$ is a proper map.

Dates et versions

hal-03526718 , version 1 (14-01-2022)

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Christian Pauly, Ana Peón-Nieto. Very stable bundles and properness of the Hitchin map. Geometriae Dedicata, 2019, 198, pp.143-145. ⟨hal-03526718⟩
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