On semistable principal bundles over a complex projective manifold

dc.creatorBiswas, Indranil
dc.creatorBruzzo, Ugo
dc.date2008-03-28
dc.date.accessioned2026-07-07T09:59:20Z
dc.date.available2026-07-07T09:59:20Z
dc.descriptionLet G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character χof P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by χis numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface.
dc.description21 pages. To appear in "International Mathematical Research Notices"
dc.identifierhttps://arxiv.org/abs/0803.4042
dc.identifierhttp://arxiv.org/abs/0803.4042
dc.identifierInternational Mathematics Research Notices, Vol. 2008, Article ID rnn035, 28 pages
dc.identifierdoi:10.1093/imrn/rnn035
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167986
dc.subjectAlgebraic Geometry
dc.subjectDifferential Geometry
dc.subject14F05, 14L10, 32L05
dc.titleOn semistable principal bundles over a complex projective manifold
dc.typetext

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