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 ${\mathbb{P}}^n(\mathbb{C})(n⩾2)$ 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 ${\mathbb{P}}^n(\mathbb{C})(n⩾5)$ share $2n+1$ hyperplanes in general position with truncated multiplicity then the map $f^1\times f^2\times f^3$ is linearly degenerate.

This paper is accepted for publication in Chinese Annals of Mathematics, Series B, Volume 39, No. 5 (2018)

Cited by in corpus (1)

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