Abstract
For a holomorphic one-form \({\xi }\) on a weakly 1-complete manifold X with certain properties, we will discuss the connectivity of the pair \((\hat{X},F^{-1}(z))\), where \(\pi :\hat{X} \rightarrow X\) is a covering map and F is a holomorphic function on \(\hat{X}\) such that \(dF=\pi ^*{\xi }\). We will also discuss the criteria about when such a manifold X admits a proper holomorphic mapping onto a Riemann surface.
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Acknowledgements
I would like to thank my advisor Professor Ramachandran who has provided me with a lot of valuable advice on this question. His patient teaching is a great encouragement for me to study math in the future.
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Communicated by Ngaiming Mok.
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Zhou, C. Lefschetz theorem for holomorphic one-forms on weakly 1-complete manifolds. Math. Ann. 382, 761–782 (2022). https://doi.org/10.1007/s00208-020-02141-y
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DOI: https://doi.org/10.1007/s00208-020-02141-y