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Uniqueness problem with truncated multiplicities in value distribution theory, II

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192, Japan, fujimoto@kappa.s.kanazawa-u.ac.jp
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Abstract

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Let 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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 155 , 1999 , pp. 161 - 188
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

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