Degeneracy and Finiteness Theorems for Meromorphic Mappings in Several Complex Variables

Abstract

The author proves that there are at most two meromorphic mappings of ℂ ^m into ℙ ⁿ(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 f ¹, f ², f ³ of ℂ ^m into ℙ ⁿ(ℂ) (n ≥ 5) share 2n+1 hyperplanes in general position with truncated multiplicity, then the map f ¹×f ²×f ³ is linearly degenerate.

Keywords

Second main theorem / Uniqueness problem / Meromorphic mapping / Multiplicity

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