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Very stable bundles and properness of the Hitchin map

· 2017 · math.AG · arXiv 1710.10152

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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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2019 1

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Non-Abelian Hodge Theory and Related Topics

math.AG · 2019-08-22 · conditional · novelty 4.0

A survey of non-Abelian Hodge theory and related moduli spaces, with a new explicit description of Simpson filtrations for rank 3 flat bundles.

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  • Non-Abelian Hodge Theory and Related Topics math.AG · 2019-08-22 · conditional · none · ref 53 · internal anchor

    A survey of non-Abelian Hodge theory and related moduli spaces, with a new explicit description of Simpson filtrations for rank 3 flat bundles.