Finite coverings of complex spaces by connected Stein open sets
The authors prove that a reduced second-countable connected complex space \(X\) of finite dimension can be covered by finitely many connected Stein open subsets, see Theorem 11. (If \(X\) is also irreducible, then the Stein subsets can be chosen to be contractible, see Theorem 10.) This answers affirmatively a question by the first author in [C. R. Acad. Sci., Paris, Sér. I 310, No. 6, 397--399 (1990; Zbl 0694.32006)]. The authors also show that, given a connected complex space \(X\), there exist a connected Stein complex space \(\tilde X\) and a surjective, holomorphic, locally biholomorphic map \(\tilde X \to X\) whose fiber has cardinality bounded by a constant depending on the dimension of \(X\), see Theorem 12. This result in the case of \(X\) irreducible and locally-irreducible has been proven in [\textit{J. E. Fornaess} and \textit{E. L. Stout}, Am. J. Math. 99, 933--960 (1977; Zbl 0384.32004)].
scientific article; zbMATH DE number 6819399
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