@article {2008,
title = {On semistable principal bundles over a complex projective manifold},
journal = {Int. Math. Res. Not. vol. 2008, article ID rnn035},
number = {arXiv.org;0803.4042v1},
year = {2008},
publisher = {Oxford University Press},
abstract = {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.},
doi = {10.1093/imrn/rnn035},
url = {http://hdl.handle.net/1963/3418},
author = {Indranil Biswas and Ugo Bruzzo}
}