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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 H 1, 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 ℓ 0 such that, for any two nondegenerate meromorphic maps f, g: ℂn → PN (ℂ) with min(ν(f, Hj ),ℓ 0) = min(ν(g, Hj ), ℓ 0) the map f × g into P N (ℂ) × PN (ℂ) is algebraically degenerate. He also shows that, for N = 2 and q = 7, there is some ℓ 0 such that the conditions min(ν(f, Hj ), ℓ 0) = min(ν(g, Hj ), ℓ 0) imply f = g for any two nondegenerate meromorphic maps f, g into P2(ℂ) and seven generic hyperplanes Hj ’s.

Information

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

References

[1] Borel, E., Sur les zéros des fonctions entiéres, Acta Math., 20 (1897), 357–396.Google Scholar
[2] Fujimoto, H., The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J., 58 (1975), 1–23.Google Scholar
[3] Fujimoto, H., A uniqueness theorem of algebraically non-degenerate meromorphic maps into PN(ℂ), Nagoya Math. J., 64 (1976), 117–147.Google Scholar
[4] Fujimoto, H., Remarks to the uniqueness problem of meromorphic maps into PN(ℂ), I, Nagoya Math. J., 71 (1978), 13–24.Google Scholar
[5] Fujimoto, H., Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into PN1(ℂ) × … × PNk(ℂ), Japan. J. Math., 11 (1985), 233–264.Google Scholar
[6] Fujimoto, H., Value distribution theory of the Gauss map of minimal surfaces in m , Aspect of Math., Vol. E21, Vieweg, Wiesbaden, 1993.Google Scholar
[7] Fujimoto, H., Uniqueness problem with truncated multiplicities in value distribution theory, Nagoya Math. J., 152 (1998), 131–152.Google Scholar
[8] Ji, S., Uniqueness problem without multiplicities in value distribution theory, Pacific J. Math., 135 (1988), 323–348.Google Scholar
[9] Shiffman, B., Introduction to the Carlson-Griffiths equidistribution theory, Lecture Notes in Math., 981, Springer-Verlag, 1983.Google Scholar
[10] Smiley, L., Geometric conditions for unicity of holomorphic curves, Contemporary Math., 25, Amer. Math. Soc. (1983), 149–154.Google Scholar
[11] Stoll, W., Introduction to value distribution theory of meromorphic maps, Lecture Notes in Math., 950 (1982), pp. 210–359.Google Scholar
[12] Toda, N., Sur une relation entre la croissance et le nombre de valeurs déficientes de fonctions algébroides ou de systémes, Kodai Math. Sem. Rep., 22 (1970), 114–121.Google Scholar