Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-24T00:00:53.941Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks to the uniqueness problem of meromorphic maps into PN(C), IV

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let H1, H2, …, HN+2 be hyperplanes in PN(C) located in general position and v1v2, … νN+2 divisors on Cn. We consider the set ℱ(Hi, νi) of all non-degenerate meromorphic maps of Cn into PN(C) such that the pull-backs ν(f, Hi) of the divisors (Hi) on PN(C) by f are equal to νi for any i = 1, 2, …, N + 2. In the previous paper [6], the author showed that =:= ℱ(Hi, νi) cannot contain more than N+ 1 algebraically independent maps. Relating to this, the following theorem will be proved.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 83 , October 1981 , pp. 153 - 181
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[1] Borel, E., Sur les zéros des fonctions entières, Acta Math., 20 (1897), 357–396.Google Scholar
[2] Fujimoto, H., On families of meromorphic maps into the complex projective space, Nagoya Math. J., 54 (1974), 21–51.Google Scholar
[3] Fujimoto, H., The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J., 58 (1975), 1–23.CrossRefGoogle Scholar
[4] Fujimoto, H., A uniqueness theorem of algebraically non-degenerate meromorphic maps into PN(C), Nagoya Math. J., 64 (1976), 117–147.Google Scholar
[5] Fujimoto, H., Remarks to the uniqueness problem of meromorphic maps into PN(C), I, II, Nagoya Math. J., 71 (1978), 13–41.Google Scholar
[6] Fujimoto, H., Remarks to the uniqueness problem of meromorphic maps into PN(C), III, Nagoya Math. J., 75 (1979), 71–85.CrossRefGoogle Scholar
[7] Green, M. L., Holomorphic maps into the complex projective space omitting hyper-planes, Trans. AMS., 169 (1972), 89–103.CrossRefGoogle Scholar
[8] Nevanlinna, R., Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris (1929).Google Scholar
[9] Stoll, W., Ganze Funktionen endlicher Ordnung mit gegebenen Nullstellenflachen, Math. Z., 57 (1953), 211–237.CrossRefGoogle Scholar
[10] Stoll, W., Normal families of non-negative divisors, Math. Z., 84 (1964), 154–218.Google Scholar
[11] Urabe, H. and Yang, C., On the zeros of an entire function which is periodic mod a non-constant entire function of order less than one, Proc. Japan Acad. Ser. A. 54 (1978), 142–144.Google Scholar
[12] Urabe, H. and Yang, C., On a characteristic property of periodic entire functions, Kodai Math. J., 3 (1979), 253–286.Google Scholar