On the value distribution of meromorphic mappings of covering spaces over Cm into algebraic varieties

Junjiro NOGUCHI

doi:10.2969/jmsj/03720295

On the value distribution of meromorphic mappings of covering spaces over C^m into algebraic varieties

Junjiro NOGUCHI

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JOURNAL FREE ACCESS

1985 Volume 37 Issue 2 Pages 295-313

DOI https://doi.org/10.2969/jmsj/03720295

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Published: 1985 Received: May 21, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : On the value distribution of meromorphic mappings of covering spaces over C^m into algebraic varieties
Right : On the value distribution of meromorphic mappings of covering spaces over C^m into algebraic varieties

Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor M. Ozawa on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Biancofiore and W. Stoll, Another proof of the lemma of the logarithmic derivative in several complex variables, Recent Developments in Several Complex Variables Ann. of Math. Studies, 100, Princeton Univ. Press, Princeton, 1981, 29-45.
2) J. Carlson and P. Griffiths, A defect relation for equidimensional holomorphic mappings between algebraic varieties, Ann. of Math., 95 (1972), 557-584.
3) H. Cartan, Sur les zéros des combinaisons linéaires de p fonctions holomorphes données, Mathematica, 7 (1933), 5-31.
4) H. Grauert and R. Remmert, Plurisubharmonische Funktionen in komplexen Räumen, Math. Z., 65(1956), 175-194.
5) P. Griffiths and J. King, Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math., 130 (1973), 145-220.
6) S. Iitaka, Logarithmic forms of algebraic varieties, J. Fac. Sci. Univ. Tokyo Sect. IA, 23 (1976), 525-544.
7) S. Iitaka, On logarithmic Kodaira dimension of algebraic varieties, Complex Analysis and Algebraic Geometry, Iwanami, Tokyo, 1977, 175-189.
8) Y. Kawamata, On Block's conjecture, Invent. Math., 57 (1980), 97-100.
9) R. Nevanlinna, Le Théorème de Picard-Borel et la théorie des fonctions méromorphes,Gauthier-Villars, Paris, 1939.
10) J. Noguchi, Meromorphic mappings of a covering space over C^m into a projective variety and defect relations, Hiroshima Math. J., 6 (1976), 265-280.
11) J. Noguchi, Holomorphic mapping into closed Riemann surfaces, Hiroshima Math. J., 6 (1976), 281-291.
12) J. Noguchi, Holomorphic curves in algebraic varieties, Hiroshima Math. J., 7 (1977), 833-853.
13) J. Noguchi, Supplement to “Holomorphic curves in algebraic varieties”. Hiroshima Math. J., 10(1980), 229-231.
14) J. Noguchi, Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties, Nagoya Math. J., 83 (1981), 213-233.
15) T. Ochiai, On holomorphic curves in algebraic varieties with ample irregularity, Invent. Math., 43(1977), 83-96.
16) F. Sakai, Defect relations and ramifications, Proc. Japan Acad., 50(1974), 723-728.
17) H. L. Selberg, Algebroide Funktionen und Umkehlfunktionen Abelscher Integrale, Avh. Norske Vid. Akad. Oslo, 8 (1934), 1-72.
18) B. Shiffman, Nevanlinna defect relations for singular divisors, Invent. Math., 31 (1975), 155-182.
19) W. Stoll, Value Distribution on Parabolic Spaces, Lecture Notes in Math., 600, Springer-Verlag, 1977.
20) W. Stoll, The Ahlfors-Weyl theory of meromorphic maps on parabolic manifolds, Value Distribution Theory, Lecture Notes in Math., 981, Springer-Verlag, 1983, 101-219.
21) G. Valiron, Sur la derivé des fonctions algebroïdes, Bull. Soc. Math. France, 59 (1931), 17-39.
22) A. L. Vitter, The lemma of the logarithmic derivative in several complex variables, Duke Math. J., 44 (1977), 89-104.
23) P. M. Wong, Holomorphic mappings into Abelian varieties, Amer. J. Math., 102 (1980), 493-501.

Right : [1] A. Biancofiore and W. Stoll, Another proof of the lemma of the logarithmic derivative in several complex variables, Recent Developments in Several Complex Variables Ann. of Math. Studies, 100, Princeton Univ. Press, Princeton, 1981, 29-45.
[2] J. Carlson and P. Griffiths, A defect relation for equidimensional holomorphic mappings between algebraic varieties, Ann. of Math., 95 (1972), 557-584.
[3] H. Cartan, Sur les zéros des combinaisons linéaires de p fonctions holomorphes données, Mathematica, 7 (1933), 5-31.
[4] H. Grauert and R. Remmert, Plurisubharmonische Funktionen in komplexen Räumen, Math. Z., 65 (1956), 175-194.
[5] P. Griffiths and J. King, Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math., 130 (1973), 145-220.
[6] S. Iitaka, Logarithmic forms of algebraic varieties, J. Fac. Sci. Univ. Tokyo Sect. IA, 23 (1976), 525-544.
[7] S. Iitaka, On logarithmic Kodaira dimension of algebraic varieties, Complex Analysis and Algebraic Geometry, Iwanami, Tokyo, 1977, 175-189.
[8] Y. Kawamata, On Block's conjecture, Invent. Math., 57 (1980), 97-100.
[9] R. Nevanlinna, Le Théorème de Picard-Borel et la théorie des fonctions méromorphes,Gauthier-Villars, Paris, 1939.
[10] J. Noguchi, Meromorphic mappings of a covering space over C^m into a projective variety and defect relations, Hiroshima Math. J., 6 (1976), 265-280.
[11] J. Noguchi, Holomorphic mapping into closed Riemann surfaces, Hiroshima Math. J., 6 (1976), 281-291.
[12] J. Noguchi, Holomorphic curves in algebraic varieties, Hiroshima Math. J., 7 (1977), 833-853.
[13] J. Noguchi, Supplement to “Holomorphic curves in algebraic varieties”, Hiroshima Math. J., 10 (1980), 229-231.
[14] J. Noguchi, Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties, Nagoya Math. J., 83 (1981), 213-233.
[15] T. Ochiai, On holomorphic curves in algebraic varieties with ample irregularity, Invent. Math., 43 (1977), 83-96.
[16] F. Sakai, Defect relations and ramifications, Proc. Japan Acad., 50 (1974), 723-728.
[17] H. L. Selberg, Algebroide Funktionen und Umkehlfunktionen Abelscher Integrale, Avh. Norske Vid. Akad. Oslo, 8 (1934), 1-72.
[18] B. Shiffman, Nevanlinna defect relations for singular divisors, Invent. Math., 31 (1975), 155-182.
[19] W. Stoll, Value Distribution on Parabolic Spaces, Lecture Notes in Math., 600, Springer-Verlag, 1977.
[20] W. Stoll, The Ahlfors-Weyl theory of meromorphic maps on parabolic manifolds, Value Distribution Theory, Lecture Notes in Math., 981, Springer-Verlag, 1983, 101-219.
[21] G. Valiron, Sur la derivé des fonctions algebroïdes, Bull. Soc. Math. France, 59 (1931), 17-39.
[22] A. L. Vitter, The lemma of the logarithmic derivative in several complex variables, Duke Math. J., 44 (1977), 89-104.
[23] P. M. Wong, Holomorphic mappings into Abelian varieties, Amer. J. Math., 102 (1980), 493-501.

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