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Moscow Mathematical Journal

Volume 16, Issue 4, October–December 2016  pp. 675–689.

Affine Connections on Complex Manifolds of Algebraic Dimension Zero

Authors:  Sorin Dumitrescu (1) and Benjamin McKay (2)
Author institution:(1) Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06108 NICE Cedex 02, France
(2) University College Cork, Cork, Ireland


We prove that any compact complex manifold with finite fundamental group and algebraic dimension zero admits no holomorphic affine connection or holomorphic conformal structure.

2010 Math. Subj. Class. Primary 53B21; Secondary 53C56, 53A55.

Keywords: Holomorphic affine connections, algebraic dimension.

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