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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 2, pp 251–272 | Cite as

Degeneracy and Finiteness Theorems for Meromorphic Mappings in Several Complex Variables

  • Si Duc QuangEmail author
Article
  • 11 Downloads

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.

Keywords

Second main theorem Uniqueness problem Meromorphic mapping Multiplicity 

2000 MR Subject Classification

32H30 32A22 30D35 

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationCau Giay, HanoiVietnam
  2. 2.Thang Long Institute of Mathematics and Applied SciencesNghiem Xuan Yem, Hoang Mai, Ha NoiVietnam

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