Degeneracy and finiteness theorems for meromorphic mappings in several complex variables
Abstract
In this article, we prove that there are at most two meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)\ (n\geqslant 2)$ 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. We also show that if three meromorphic mappings $f^1,f^2,f^3$ of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)\ (n\geqslant 5)$ share $2n+1$ hyperplanes in general position with truncated multiplicity then the map $f^1\times f^2\times f^3$ is linearly degenerate.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.5533
 Bibcode:
 2014arXiv1402.5533Q
 Keywords:

 Mathematics  Complex Variables;
 32H30;
 32A22 (Primary) 30D35 (Secondary)
 EPrint:
 This paper is accepted for publication in Chinese Annals of Mathematics, Series B, Volume 39, No. 5 (2018)