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References (4)
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M. Atiyah (1957)
Complex analytic connections in fibre bundlesTransactions of the American Mathematical Society, 85
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H. Azad, I. Biswas (2002)
On holomorphic principal bundles over a compact Riemann surface admitting a flat connectionMathematische Annalen, 322
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A. Ramanathan (1975)
Stable principal bundles on a compact Riemann surfaceMathematische Annalen, 213
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A. Weil (1979)
Généralisation des fonctions abéliennes
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/S0024609303002182
- Publisher site
- See Article on Publisher Site
Abstract
Holomorphic principal bundles over a compact Riemann surface X that admits a flat connection are considered. A holomorphic G‐bundle over X, where G is a connected semisimple linear algebraic group over C, admits a flat connection if and only if the adjoint vector bundle admits one. More generally, for a complex reductive group G, the necessary and sufficient condition on a G‐bundle to admit a flat connection is described. This simplifies the criterion obtained by the authors and given in Math. Ann. 322 (2002) 333–346. 2000 Mathematics Subject Classification 53C05, 32L05.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Jul 1, 2003