%0 Journal Article
%J Int. Math. Res. Not. vol. 2008, article ID rnn035
%D 2008
%T On semistable principal bundles over a complex projective manifold
%A Indranil Biswas
%A Ugo Bruzzo
%X Let 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 \\\\chi of 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 \\\\chi is 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.
%B Int. Math. Res. Not. vol. 2008, article ID rnn035
%I Oxford University Press
%G en_US
%U http://hdl.handle.net/1963/3418
%1 917
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-12T09:53:34Z\\nNo. of bitstreams: 1\\n0803.4042v1.pdf: 273878 bytes, checksum: 8f729aa65d9cebf234016c17cacfedbc (MD5)
%R 10.1093/imrn/rnn035