Flat holomorphic connections on principal bundles over a projective manifold

Biswas, Indranil; Subramanian, S.

doi:10.1090/S0002-9947-04-03567-6

Flat holomorphic connections on principal bundles over a projective manifold
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by Indranil Biswas and S. Subramanian

Trans. Amer. Math. Soc. 356 (2004), 3995-4018

DOI: https://doi.org/10.1090/S0002-9947-04-03567-6

Published electronically: February 27, 2004

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Abstract:

Let $G$ be a connected complex linear algebraic group and $R_u(G)$ its unipotent radical. A principal $G$–bundle $E_G$ over a projective manifold $M$ will be called polystable if the associated principal $G/R_u(G)$–bundle is so. A $G$–bundle $E_G$ over $M$ is polystable with vanishing characteristic classes of degrees one and two if and only if $E_G$ admits a flat holomorphic connection with the property that the image in $G/R_u(G)$ of the monodromy of the connection is contained in a maximal compact subgroup of $G/R_u(G)$.

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