Abstract
Let M be a complete and connected Kähler manifold whose universal covering is biholomorphic to a ball in \({\mathbb {C}}^m\). In this article, we investigate algebraic dependence of three meromorphic mappings from M into \({\mathbf {P}}^n({\mathbb {C}})\) sharing hyperplanes in subgeneral position. In addition, we study linear degenerates of the map \(f^1\times f^2 \times f^3\) where \(f_1, f_2\) and \(f_3\) are meromorphic mappings of M into \({\mathbf {P}}^n(\mathbb C)\ (n \geqslant 5)\) sharing hyperplanes in subgeneral position with truncated multiplicity.
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Acknowledgements
The authors wish to express their thanks to the referee for his/her valuable suggestions and comments. This work was done during a stay of the second author at the Vietnam Institute for Advanced Study in Mathematics (VIASM). The authors would like to thank VIASM for partial support, and the staff of VIASM for their hospitality.
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Communicated by Pekka Koskela.
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The research of the authors is supported by an NAFOSTED grant of Vietnam (Grant no. 101.04-2017.317).
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Nguyen, T.N., Pham, D.T. On Degeneracy of Three Meromorphic Mappings from Complete Kähler Manifolds into Projective Spaces. Comput. Methods Funct. Theory 19, 353–382 (2019). https://doi.org/10.1007/s40315-019-00284-x
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DOI: https://doi.org/10.1007/s40315-019-00284-x