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Semistability vs. nefness for (Higgs) vector bundles

U. Bruzzo·D. Hernandez Ruiperez
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Abstract

According to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E.

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U. Bruzzo, D. Hernandez Ruiperez. 2005-04-20. Semistability vs. nefness for (Higgs) vector bundles. https://doi.org/10.1016/j.difgeo.2005.12.007

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