Soit M une variété complexe compacte connexe, munie d'une submersion holomorphe , 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.
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.
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@article{CRMATH_2007__344_9_577_0, author = {Biswas, Indranil and Iyer, Jaya N.}, 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}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.03.030/} }
TY - JOUR AU - Biswas, Indranil AU - Iyer, Jaya N. TI - Holomorphic connections on some complex manifolds JO - Comptes Rendus. Mathématique PY - 2007 SP - 577 EP - 580 VL - 344 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.03.030/ DO - 10.1016/j.crma.2007.03.030 LA - en ID - CRMATH_2007__344_9_577_0 ER -
%0 Journal Article %A Biswas, Indranil %A Iyer, Jaya N. %T Holomorphic connections on some complex manifolds %J Comptes Rendus. Mathématique %D 2007 %P 577-580 %V 344 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.03.030/ %R 10.1016/j.crma.2007.03.030 %G en %F CRMATH_2007__344_9_577_0
Biswas, Indranil; Iyer, Jaya N. Holomorphic connections on some complex manifolds. Comptes Rendus. Mathématique, Tome 344 (2007) no. 9, pp. 577-580. doi : 10.1016/j.crma.2007.03.030. http://archive.numdam.org/articles/10.1016/j.crma.2007.03.030/
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