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A Bochner-Hartogs type theorem for coverings of compact Kähler manifolds. (English) Zbl 0955.32018
From the text: Let $$M$$ be a connected noncompact complex manifold. We say $$M$$ satisfies the Bochner-Hartogs property if $$H^1_C (H, {\mathcal O}_M)=0$$.
Main Theorem. Let $$X$$ be a connected compact Kähler manifold. Let $$\widetilde X$$ be a Galois covering of $$X$$ with infinite covering group $$\Gamma$$ of more than quadratic growth. If $$\widetilde X$$ admits a nonconstant holomorphic function, then either $$\widetilde X$$ maps properly onto a Riemann surface or it satisfies the Bochner-Hartogs property.

##### MSC:
 32J27 Compact Kähler manifolds: generalizations, classification 53C55 Global differential geometry of Hermitian and Kählerian manifolds
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