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Numerically flat Higgs vector bundles

Ugo Bruzzo·Beatriz Graña Otero
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Abstract

After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.

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Ugo Bruzzo, Beatriz Graña Otero. 2006-03-21. Numerically flat Higgs vector bundles. https://doi.org/10.1142/s0219199707002526

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