On semistable principal bundles over a complex projective manifold, II

Details On semistable principal bundles over a complex projective manifold, II On semistable principal bundles over a complex projective manifold, II

2009-09-25

arxiv.org/abs/0909.4802v1

Geom. Dedicata 146 (2010), 27-41

Mathematics

Algebraic Geometry

15 pages

Scientific paper

Let (X, \omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.

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