Bogomolov inequality for Higgs parabolic bundles (Q1965132)

The author shows that there are restrictions on the structure of a smooth projective variety supporting a semistable Higgs logarithmic vector bundle which is unstable in the ordinary sense. This cannot happen on Fano manifolds with semistable tangent bundle. A semistable Higgs parabolic vector bundle of rank 2 over a smooth projective variety of dimension\(>1\) is shown to satisfy the ``parabolic'' Bogomolov inequality.