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arXiv · 2004.09217

Vanishing Chern classes for numerically flat Higgs bundles

Armando Capasso
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Abstract

I consider Higgs bundles satisfying a notion of ampleness that was introduce Bruzzo, Gra\~na Otero and Hern\'andez Ruip\'erez, and prove that the Chern classes of rank $r$ H-ample Higgs bundles over dimension $n$, polarized, smooth, complex, projective varieties are positive under opportune hypothesis. I extend this to non-negativeness of Chern classes of all numerically effective Higgs bundles; and use this condition to prove the vanishing of Chern classes of numerically flat Higgs bundles.

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Armando Capasso. 2020-04-20. Vanishing Chern classes for numerically flat Higgs bundles. https://arxiv.org/abs/2004.09217

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