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Degeneracy and Finiteness Theorems for Meromorphic Mappings in Several Complex Variables

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Abstract

The author proves that there are at most two meromorphic mappings of ℂm into ℙn(ℂ) (n ≥ 2) sharing 2n+2 hyperplanes in general position regardless of multiplicity, where all zeros with multiplicities more than certain values do not need to be counted. He also shows that if three meromorphic mappings f1, f2, f3 of ℂm into ℙn(ℂ) (n ≥ 5) share 2n+1 hyperplanes in general position with truncated multiplicity, then the map f1×f2×f3 is linearly degenerate.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, 136-Xuan Thuy, Cau Giay, Hanoi, Vietnam

    Si Duc Quang

  2. Thang Long Institute of Mathematics and Applied Sciences, Nghiem Xuan Yem, Hoang Mai, Ha Noi, Vietnam

    Si Duc Quang

Authors
  1. Si Duc Quang
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Correspondence to Si Duc Quang.

Additional information

This work was supported by the Vietnam National Foundation for Science and Technology Development (No. 101.04-2018.01).

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Quang, S.D. Degeneracy and Finiteness Theorems for Meromorphic Mappings in Several Complex Variables. Chin. Ann. Math. Ser. B 40, 251–272 (2019). https://doi.org/10.1007/s11401-019-0131-y

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  • DOI: https://doi.org/10.1007/s11401-019-0131-y

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