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Coverings of locally conformally Kähler complex spaces

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In this paper, we study the properties of coverings of locally conformally Kähler (LCK) spaces with singularities. We begin by proving that a space is LCK if any only if its universal cover is Kähler, thereby generalizing a result from Ioniţă and Preda (Manuscripta Math, https://doi.org/10.1007/s00229-019-01141-w, 2019). We then show that a complex space which projects over an LCK space with discrete fibers must also carry an LCK structure.

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Acknowledgements

We would like to thank Liviu Ornea for his support and suggestions, Victor Vuletescu for helpful discussions about LCK spaces with singularities and Alexandra Otiman for carefully reading the paper and her comments.

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  1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21 Calea Griviţei Street, 010702, Bucharest, Romania

    Ovidiu Preda & Miron Stanciu

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  1. Ovidiu Preda
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  2. Miron Stanciu
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Correspondence to Miron Stanciu.

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Ovidiu Preda was partially supported by a Grant of Ministry of Research and Innovation, CNCS-UEFISCDI, project number PN-III-P1-1.1-PD-2016-0182, within PNCDI III.

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Preda, O., Stanciu, M. Coverings of locally conformally Kähler complex spaces. Math. Z. 298, 639–651 (2021). https://doi.org/10.1007/s00209-020-02616-3

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