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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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