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arXiv · 1710.10152

Very stable bundles and properness of the Hitchin map

Christian Pauly·Ana Peón-Nieto
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Abstract

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.

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Christian Pauly, Ana Peón-Nieto. 2017-10-27. Very stable bundles and properness of the Hitchin map. https://doi.org/10.1007/s10711-018-0333-6.

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