On semistable principal bundles over a complex projective manifold, II

Biswas, Indranil ; Bruzzo, Ugo (2010) On semistable principal bundles over a complex projective manifold, II Geometriae Dedicata, 146 (1). pp. 27-41. ISSN 0046-5755

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Official URL: http://www.springerlink.com/content/x72323505mhg26...

Related URL: http://dx.doi.org/10.1007/s10711-009-9424-8


Let (X, ω) be a compact connected Kahler manifold of complex dimension d and EG → X a holomorphic principal G-bundle, 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 ⊂ G and a holomorphic reduction of structure group EP ⊂ EG to P, such that the corresponding L(P)/Z(G)-bundle EL(P)/Z(G): = EP(L(P)/Z(G) → X admits a unitary flat connection, where L(P) is the Levi quotient of P. (2) The adjoint vector bundle ad(E G) is numerically flat. (3) The principal G-bundle E G is pseudostable, and ∫X C2(ad(EGd-2 = 0 If X is a complex projective manifold, and ω represents a rational cohomology class, then the third statement is equivalent to the statement that E G is semistable with c2(ad(EG )) = 0.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
Keywords:Principal Bundle; Pseudostability; Numerical Effectiveness
ID Code:3638
Deposited On:18 Oct 2010 10:16
Last Modified:27 Jan 2011 06:20

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