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      Connexions affines et projectives sur les surfaces complexes compactes

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          Abstract

          We prove that holomorphic normal projective connections on compact complex surfaces are flat. We show that a holomorphic torsion-free affine connection \(\nabla\) on a compact complex surface is locally modelled on a translations-invariant affine connection on \(\C^2\), except if \(\nabla\) is a generic connection on a principal elliptic bundle over a Riemann surface of genus \(g \geq 2\), with odd first Betti number. In the last case, the local Killing Lie algebra is of dimension one, generated by the fundamental vector field of the principal fibration.

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          Author and article information

          Journal
          19 May 2008
          Article
          0805.2816
          787e43ea-3832-4e7d-9ae6-83dacf440be0

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          53B21;53C56;53A55
          20 pages, french
          math.DG math.CV

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