Filtrations of numerically flat Higgs bundles and curve semistable Higgs bundles on Calabi-Yau manifolds

Abstract

We consider Higgs bundles satisfying a notion of numerical flatness (H-nflatness) that was previously introduced, 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 manifolds have vanishing discriminant.

arXiv comment9 pages. v2: 12 pages, details (especially to the proof of Lemma 3.1), explanations and comments added; typos corrected