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Transactions of the American Mathematical Society
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Flat holomorphic connections on principal bundles over a projective manifold

Author(s): Indranil Biswas; S. Subramanian
Journal: Trans. Amer. Math. Soc. 356 (2004), 3995-4018.
MSC (2000): Primary 53C07, 32L05, 14J60
Posted: February 27, 2004
MathSciNet review: 2058516
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Abstract | References | Similar articles | Additional information

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
Email: indranil@math.tifr.res.in

S. Subramanian
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Email: subramnn@math.tifr.res.in

DOI: 10.1090/S0002-9947-04-03567-6
PII: S 0002-9947(04)03567-6
Keywords: Principal bundle, unitary connection, polystability
Received by editor(s): April 23, 2003
Received by editor(s) in revised form: June 24, 2003
Posted: February 27, 2004
Copyright of article: Copyright 2004, American Mathematical Society




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