00836nas a2200121 4500008004100000245009000041210007300131260001300204520040500217100001600622700002500638856005100663 2014 en d00aApproximate Hermitian–Yang–Mills structures on semistable principal Higgs bundles0 aApproximate Hermitian–Yang–Mills structures on semistable princi bSpringer3 aWe generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://urania.sissa.it/xmlui/handle/1963/3464501465nas 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/1963/363801055nas a2200109 4500008004300000245006600043210006600109520069300175100001600868700002500884856003600909 2007 en_Ud 00aMetrics on semistable and numerically effective Higgs bundles0 aMetrics on semistable and numerically effective Higgs bundles3 aWe consider fibre metrics on Higgs vector bundles on compact K\\\\\\\"ahler manifolds, providing notions of numerical effectiveness and numerical flatness in terms of such metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they admit filtrations whose quotients are stable flat Higgs bundles. We compare these definitions with those previously given in the case of projective varieties. Finally we study the relations between numerically effectiveness and semistability, providing semistability criteria for Higgs bundles on projective manifolds of any dimension.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/184000810nas a2200109 4500008004300000245004200043210004200085520049600127100001600623700002500639856003600664 2007 en_Ud 00aNumerically flat Higgs vector bundles0 aNumerically flat Higgs vector bundles3 aAfter providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/175700296nas a2200097 4500008004300000245003900043210003900082100001600121700002500137856003600162 2007 en_Ud 00aSemistable principal Higgs bundles0 aSemistable principal Higgs bundles1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/2533