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arXiv · 1402.5533

Degeneracy and finiteness theorems for meromorphic mappings in several complex variables

Si Duc Quang
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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.

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Si Duc Quang. 2014-02-22. Degeneracy and finiteness theorems for meromorphic mappings in several complex variables. https://doi.org/10.1007/s11401-019-0131-y

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