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Transactions of the American Mathematical Society

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Flat holomorphic connections on principal bundles over a projective manifold

Authors: Indranil Biswas and S. Subramanian
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 3995-4018
MSC (2000): Primary 53C07, 32L05, 14J60
Published electronically: February 27, 2004
MathSciNet review: 2058516
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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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Additional Information

Indranil Biswas
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

S. Subramanian
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

Keywords: Principal bundle, unitary connection, polystability
Received by editor(s): April 23, 2003
Received by editor(s) in revised form: June 24, 2003
Published electronically: February 27, 2004
Article copyright: © Copyright 2004 American Mathematical Society