Uniqueness problem with truncated multiplicities in value distribution theory, II

Abstract

AbstractLet H1, H2,…,Hq be hyperplanes in PN (ℂ) in general position. Previously, the author proved that, in the case where q ≥ 2N + 3, the condition ν(f,Hj) = ν(g, Hj) imply f = g for algebraically nondegenerate meromorphic maps f, g: ℂn → PN(ℂ), where ν(f, Hj) denote the pull-backs of Hj through f considered as divisors. In this connection, it is shown that, for q ≥ 2N + 2, there is some integer ℓ0 such that, for any two nondegenerate meromorphic maps f, g: ℂn → PN(ℂ) with min(ν(f, Hj),ℓ0) = min(ν(g, Hj), ℓ0) the map f × g into PN(ℂ) × PN(ℂ) is algebraically degenerate. He also shows that, for N = 2 and q = 7, there is some ℓ0 such that the conditions min(ν(f, Hj), ℓ0) = min(ν(g, Hj), ℓ0) imply f = g for any two nondegenerate meromorphic maps f, g into P2(ℂ) and seven generic hyperplanes Hj’s.