Abstract
In this note, by using the Yang–Mills–Higgs flow, we show that semistable Higgs bundles with vanishing first and second Chern numbers over compact Käher manifolds must admit a filtration whose quotients are Hermitian flat Higgs bundles. This generalizes a result of Simpson for compact projective manifolds to the compact Kähler case.
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Y. Nie and X. Zhang were supported in part by NSF in China, Nos. 11131007, 11426236.
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Nie, Y., Zhang, X. A note on semistable Higgs bundles over compact Kähler manifolds. Ann Glob Anal Geom 48, 345–355 (2015). https://doi.org/10.1007/s10455-015-9474-0
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DOI: https://doi.org/10.1007/s10455-015-9474-0