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On holomorphic maps into compact non-Kähler manifolds. (English) Zbl 1077.32003
Author’s abstract: We study the extension problem of holomorphic maps $$\sigma : H \to X$$ of a Hartogs domain $$H$$ with values in a complex manifold $$X$$. For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain $$\Omega_ \sigma$$ of extension for $$\sigma$$ over $$\Delta$$ is contained in a subdomain of $$\Delta$$. For such manifolds, we define, in this paper, an invariant Hex$$_n(X)$$ using the Hausdorff dimensions of the singular sets of $$\sigma$$’s and study its properties to deduce informations on the complex structure of $$X$$.

##### MSC:
 32D15 Continuation of analytic objects in several complex variables 32D10 Envelopes of holomorphy 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables 32J17 Compact complex $$3$$-folds 32J18 Compact complex $$n$$-folds
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