Holomorphic connections on some complex manifolds

Indranil Biswas; Jaya N. Iyer

doi:10.1016/j.crma.2007.03.030

Algebraic Geometry

Holomorphic connections on some complex manifolds

Presented by: Jean-Pierre Demailly

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

Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 577-580.

Abstract
Résumé

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 $M \to T$ , 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: 2006-02-01
Accepted: 2007-03-20
Published online: 2007-04-30

DOI: 10.1016/j.crma.2007.03.030

Author's affiliations:

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

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     title = {Holomorphic connections on some complex manifolds},
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.030/

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