Mathematics – Algebraic Geometry
Scientific paper
2008-03-28
International Mathematics Research Notices, Vol. 2008, Article ID rnn035, 28 pages
Mathematics
Algebraic Geometry
21 pages. To appear in "International Mathematical Research Notices"
Scientific paper
10.1093/imrn/rnn035
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.
Biswas Indranil
Bruzzo Ugo
No associations
LandOfFree
On semistable principal bundles over a complex projective manifold does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On semistable principal bundles over a complex projective manifold, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On semistable principal bundles over a complex projective manifold will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-173631