Algebraic Geometry
Holomorphic connections on some complex manifolds
Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 577-580.

Let M be a compact connected complex manifold equipped with a holomorphic submersion to a complex torus such that the fibers are all rationally connected. Then any holomorphic vector bundle over M admitting a holomorphic connection actually admits a flat holomorphic connection. A similar statement is valid for any finite quotient of M.

Soit M une variété complexe compacte connexe, munie d'une submersion holomorphe MT, où T est un tore complexe, telle que les fibres soient rationnellement connexes. Soit E un fibré vectoriel holomorphe sur M admettant une connexion. Alors E admet une connexion holomorphe plate. Un énoncé similaire vaut pour tout quotient fini de M.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.03.030
Biswas, Indranil 1; Iyer, Jaya N. 2

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
2 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
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Biswas, Indranil; Iyer, Jaya N. Holomorphic connections on some complex manifolds. Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 577-580. doi : 10.1016/j.crma.2007.03.030. http://www.numdam.org/articles/10.1016/j.crma.2007.03.030/

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