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We consider Higgs bundles satisfying a notion of numerical flatness (H-nflatness) that was introduced in [5; 4], and show that they have Jordan-Hölder filtrations whose quotients are stable, locally free and H-nflat. This is applied to show that curve semistable Higgs bundles on simply connected Calabi–Yau varieties have vanishing discriminant.

Filtrations of numerically flat Higgs bundles and curve semistable Higgs bundles on Calabi–Yau varieties