Comptes Rendus
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.

Published online:
DOI: 10.1016/j.crma.2007.03.030

Indranil Biswas 1; Jaya N. Iyer 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
     author = {Indranil Biswas and Jaya N. Iyer},
     title = {Holomorphic connections on some complex manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {577--580},
     publisher = {Elsevier},
     volume = {344},
     number = {9},
     year = {2007},
     doi = {10.1016/j.crma.2007.03.030},
     language = {en},
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%A Indranil Biswas
%A Jaya N. Iyer
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%J Comptes Rendus. Mathématique
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Indranil Biswas; Jaya N. Iyer. 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.

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