%0 Journal Article
%D 2014
%T Approximate Hermitian–Yang–Mills structures on semistable principal Higgs bundles
%A Ugo Bruzzo
%A Beatriz Grana-Otero
%X We 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.
%I Springer
%G en
%U http://urania.sissa.it/xmlui/handle/1963/34645
%1 34849
%2 Mathematics
%$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-14T16:50:03Z
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%R 10.1007/s10455-014-9433-1
%0 Journal Article
%J Advances in Mathematics 226 (2011) 3655-3676
%D 2011
%T Semistable and numerically effective principal (Higgs) bundles
%A Ugo Bruzzo
%A Beatriz Grana-Otero
%X We 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.
%B Advances in Mathematics 226 (2011) 3655-3676
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/3638
%1 666
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-18T12:30:35Z\\r\\nNo. of bitstreams: 1\\r\\nBruzzo_Otero.pdf: 270209 bytes, checksum: 843961bd72149ca85c9b100395b70ed1 (MD5)
%R 10.1016/j.aim.2010.10.026
%0 Journal Article
%J J. Reine Angew. Math. 612 (2007) 59-79
%D 2007
%T Metrics on semistable and numerically effective Higgs bundles
%A Ugo Bruzzo
%A Beatriz Grana-Otero
%X We 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.
%B J. Reine Angew. Math. 612 (2007) 59-79
%G en_US
%U http://hdl.handle.net/1963/1840
%1 2376
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-06-19T08:20:16Z\\nNo. of bitstreams: 1\\nmath.DG-0605659.pdf: 242976 bytes, checksum: b5e79cfd73f6c6533a0ae12bad3e3c90 (MD5)
%R 10.1515/CRELLE.2007.084
%0 Report
%D 2007
%T Numerically flat Higgs vector bundles
%A Ugo Bruzzo
%A Beatriz Grana-Otero
%X After 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.
%B Commun. Contemp. Math. 9 (2007) 437-446
%G en_US
%U http://hdl.handle.net/1963/1757
%1 2787
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-21T15:59:56Z\\nNo. of bitstreams: 1\\n39_2005_fm.pdf: 192887 bytes, checksum: 1d32aff78ef27b80046dfc391135d55a (MD5)
%R 10.1142/S0219199707002526
%0 Report
%D 2007
%T Semistable principal Higgs bundles
%A Ugo Bruzzo
%A Beatriz Grana-Otero
%G en_US
%U http://hdl.handle.net/1963/2533
%1 1585
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-17T09:52:22Z\\nNo. of bitstreams: 1\\nPrincHiggs-2.pdf: 197562 bytes, checksum: 44797463786b3c14408f7d1898531202 (MD5)