Holomorphic connections on some complex manifolds

Biswas, Indranil ; Iyer, Jaya N. (2007) Holomorphic connections on some complex manifolds Comptes Rendus Mathematique, 344 (9). pp. 577-580. ISSN 1631-073X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S16310...

Related URL: http://dx.doi.org/10.1016/j.crma.2007.03.030

Abstract

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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