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Article overview
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On semistable principal bundles over a complex projective manifold | | Indranil Biswas
; Ugo Bruzzo
; | | Date: |
28 Mar 2008 | | 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. | | Source: | arXiv, 0803.4042 | | Services: | Forum | Review | PDF | Favorites | |
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