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Finite coverings of complex spaces by connected Stein open sets

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Abstract

We prove that every reduced, second countable, connected complex space X can be written as a finite union of connected Stein open subsets. If X is irreducible, we show that these Stein open subsets can be chosen to be contractible. We also prove that there exist a connected Stein space \({{\tilde{X}}}\) and a surjective holomorphic, locally biholomorphic map \(p:{{\tilde{X}}}\rightarrow X\) with finite fiber.

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Acknowledgements

Both authors were partially supported by CNCS grant PN-III-P4-ID-PCE- 2016-0341.

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Authors and Affiliations

  1. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Mihnea Colţoiu & Cezar Joiţa

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  1. Mihnea Colţoiu
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  2. Cezar Joiţa
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Correspondence to Cezar Joiţa.

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Dedicated to the memory of our friend Adrian Constantinescu.

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Colţoiu, M., Joiţa, C. Finite coverings of complex spaces by connected Stein open sets. Math. Z. 287, 929–946 (2017). https://doi.org/10.1007/s00209-017-1852-9

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  • DOI: https://doi.org/10.1007/s00209-017-1852-9

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