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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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