多复变数亚纯映射的退化与有限性定理
Degeneracy and finiteness theorems for meromorphic mappings in several complex variables
摘要：
本文证明了$\mathbb C^m$到$\mathbb P^n(\mathbb C)\ (n\geqslant 2)$的亚纯映射在一般位置上至多有两个与重数无关的共$2n+2$超平面，其中重数大于一定值的所有零点都不需要计数.我们还证明了如果$\mathbb C^m$到$\mathbb P^n(\mathbb C)\ (n\geqslant 5)$的三个亚纯映射$2n+1$在一般位置上具有截断重数，则映射$f^1\times f^2\times f^3$是线性退化的.
英文摘要：
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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