01465nas a2200121   4500008004300000245006700043210006500110260001300175520107800188100001601266700002501282856003601307       2011                        en_Ud  00aSemistable and numerically effective principal (Higgs) bundles0 aSemistable and numerically effective principal Higgs bundles  bElsevier3 aWe study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if certain line bundles, obtained from some characters of the parabolic subgroups of G, are numerically effective. One also proves that these conditions are met for semistable principal Higgs bundles whose adjoint bundle has vanishing second Chern class.\\r\\n\\r\\nIn a second part of the paper, we introduce notions of numerical effectiveness and numerical flatness for principal (Higgs) bundles, discussing their main properties. For (non-Higgs) principal bundles, we show that a numerically flat principal bundle admits a reduction to a Levi factor which has a flat Hermitian–Yang–Mills connection, and, as a consequence, that the cohomology ring of a numerically flat principal bundle with coefficients in R is trivial. To our knowledge this notion of numerical effectiveness is new even in the case of (non-Higgs) principal bundles.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz  uhttp://hdl.handle.net/1963/3638