Title | On semistable principal bundles over a complex projective manifold |

Publication Type | Journal Article |

Year of Publication | 2008 |

Authors | Biswas, I, Bruzzo, U |

Journal | Int. Math. Res. Not. vol. 2008, article ID rnn035 |

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. |

URL | http://hdl.handle.net/1963/3418 |

DOI | 10.1093/imrn/rnn035 |

## On semistable principal bundles over a complex projective manifold

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