Degeneracy and Finiteness Theorems for Meromorphic Mappings in Several Complex Variables

Citation:

Si Duc QUANG.Degeneracy and Finiteness Theorems for Meromorphic Mappings in Several Complex Variables[J].Chinese Annals of Mathematics B,2019,40(2):251~272
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Authors:

Si Duc QUANG;

Foundation:

This work was supported by the Vietnam National Foundation for Science and Technology Development (No.101.04-2018.01).
Abstract: The author proves that there are at most two meromorphic mappings of $\C^m$ into $\P^n(\C)\ (n\geq 2)$ 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 $f^1,f^2,f^3$ of $\C^m$ into $\P^n(\C)\ (n\geq 5)$ share $2n+1$ hyperplanes in general position with truncated multiplicity, then the map $f^1\times f^2\times f^3$ is linearly degenerate.

Keywords:

Second main theorem, Uniqueness problem, Meromorphic mapping, Multiplicity

Classification:

32H30, 32A22, 30D35
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