On semistable principal bundles over a complex projective manifold
| dc.creator | Biswas, Indranil | |
| dc.creator | Bruzzo, Ugo | |
| dc.date | 2008-03-28 | |
| dc.date.accessioned | 2026-07-07T09:59:20Z | |
| dc.date.available | 2026-07-07T09:59:20Z | |
| dc.description | 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 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.description | 21 pages. To appear in "International Mathematical Research Notices" | |
| dc.identifier | https://arxiv.org/abs/0803.4042 | |
| dc.identifier | http://arxiv.org/abs/0803.4042 | |
| dc.identifier | International Mathematics Research Notices, Vol. 2008, Article ID rnn035, 28 pages | |
| dc.identifier | doi:10.1093/imrn/rnn035 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167986 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 14F05, 14L10, 32L05 | |
| dc.title | On semistable principal bundles over a complex projective manifold | |
| dc.type | text |