Degeneracy and Finiteness Theorems for Meromorphic Mappings in Several Complex Variables
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The author proves that there are at most two meromorphic mappings of ℂm into ℙn(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. He also shows that if three meromorphic mappings f1, f2, f3 of ℂm into ℙn(ℂ) (n ≥ 5) share 2n+1 hyperplanes in general position with truncated multiplicity, then the map f1×f2×f3 is linearly degenerate.
KeywordsSecond main theorem Uniqueness problem Meromorphic mapping Multiplicity
2000 MR Subject Classification32H30 32A22 30D35
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