On Holomorphic Principal Bundles Over a Compact Riemann Surface Admitting a Flat Connection, II |
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| Authors: | Azad Hassan; Biswas Indranil |
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| Institution: | Department of Mathematical Sciences, King Fahd University Dhahran 31261, Saudi Arabia; hassanaz{at}kfupm.edu.sa
School of Mathematics, Tata Institute of Fundamental Research Homi Bhabha Road, Bombay 400005, India; indranil{at}math.tifr.res.in |
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| Abstract: | Holomorphic principal bundles over a compact Riemann surfaceX that admits a flat connection are considered. A holomorphicG-bundle over X, where G is a connected semisimple linear algebraicgroup over C, admits a flat connection if and only if the adjointvector bundle admits one. More generally, for a complex reductivegroup G, the necessary and sufficient condition on a G-bundleto admit a flat connection is described. This simplifies thecriterion obtained by the authors and given in Math. Ann. 322(2002) 333–346. 2000 Mathematics Subject Classification53C05, 32L05. |
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