Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and hyperbolic fibre spaces

Makoto SUZUKI

doi:10.2969/jmsj/04640681

Makoto SUZUKI

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JOURNAL FREE ACCESS

1994 Volume 46 Issue 4 Pages 681-698

DOI https://doi.org/10.2969/jmsj/04640681

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Published: 1994 Received: October 26, 1992 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: CITATION Details: Wrong : 1) A. Douady, Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Ann. Inst. Fourier (Grenoble), 16 (1966), 1-95.
2) Y. Imayoshi, Generalization of de Franchis theorem, Duke Math. J., 50 (1983), 393-408.
3) Y. Imayoshi, Holomorphic maps of projective algebraic manifolds into C-hyperbolic manifolds, J. Math. Soc. Japan, 46 (1994), 289-307,
4) Y. Imayoshi and H, Shiga, A finiteness theorem for holomorphic families of Riemann surfaces, in Proc. Holomorphic Functions and Moduli, MSRI Berkeley, 1986.
5) S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York, 1970.
6) S. Kobayashi and T. Ochiai, Satake compactification and the great Picard theorem, J. Math. Soc. Japan, 23 (1971), 340-350.
7) A. Kodama, On bimeromorphic automorphisms of hyperbolic complex spaces, Nagoya Math. J., 73 (1979), 1-5.
8) S. Lang, Higher dimensional Diophantine problems, Bull. Amer. Math. Soc., 80 (1974), 779-787.
9) S. Lang, Introduction to Complex Hyperbolic Spaces, Springer-Verlag, New York-Berlin-Heidelberg, 1987.
10) Ju.I. Manin, Rational points of algebraic curves over function fields, Izv. Akad. Nauk SSSR Ser. Mat., 27 (1963), 1395-1440.
11) T. Miyano and J. Noguchi, Moduli spaces of harmonic and holomorphic mappings and Diophantine geometry, in Prospects in Complex Geometry, Proc. 25th Taniguchi International Symposium, Katata/Kyoto, 1989, Lecture Notes in Math., 1468, Springer-Verlag, Heidelberg, 1991.
12) J. Noguchi, Hyperbolic fibre spaces and Mordell's conjecture over function fields, Publ. Res. Inst. Math. Sci. Kyoto University, 21 (1985), 27-46.
13) J. Noguchi, Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces, Invent. Math., 93 (1988), 15-34.
14) J. Noguchi, Hyperbolic manifolds and Diophantine geometry, Sugaku Expositions,Amer. Math. Soc., Providence, Rhode Island, 1991. (Translation of Japanese version, Sugaku, 41 (1989), 320-334.)
15) J. Noguchi, An example of a hyperbolic fiber space without hyperbolic embedding into compactification, Proceedings of Osaka International Conference, Osaka 1990.
16) J. Noguchi, Meromorphic mappinngs into compact hyperbolic complex spaces and geometric Diophantine problems, Internat. J. Math., 3 (1992), 277-289, and its correction (to appear).
17) J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, Transl. Math. Monographs., 80, Amer. Math. Soc., Providence, Rhode Island, 1990.
18) J. Noguchi and T. Sunada, Finiteness of the family of rational and meromorphic mappings into algebraic varieties, Amer. J. Math., 104 (1982), 887-900.
19) T. Sunada, Holomorphic mappings into a compact quotient of symmetric bounded domain, Nagoya Math. J., 64 (1976), 159-175.
20) R. Tsushima, Rational maps to varieties of hyperbolic type, Proc. Japan Acad. Ser. A, 55 (1979), 95-100.
21) T. Urata, Holomorphic mappings into taut complex analytic spaces, Tohoku Math. J., 31 (1979), 349-353.
22) M. G. Zaidenberg, A function-field analog of the Mordell conjecture: A noncompact version, Math. USSR-Izv., 35 (1990), 61-81.

Right : [1] A. Douady, Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Ann. Inst. Fourier (Grenoble), 16 (1966), 1-95.
[2] Y. Imayoshi, Generalization of de Franchis theorem, Duke Math. J., 50 (1983), 393-408.
[3] Y. Imayoshi, Holomorphic maps of projective algebraic manifolds into C-hyperbolic manifolds, J. Math. Soc. Japan, 46 (1994), 289-307,
[4] Y. Imayoshi and H, Shiga, A finiteness theorem for holomorphic families of Riemann surfaces, in Proc. Holomorphic Functions and Moduli, MSRI Berkeley, 1986.
[5] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York, 1970.
[6] S. Kobayashi and T. Ochiai, Satake compactification and the great Picard theorem, J. Math. Soc. Japan, 23 (1971), 340-350.
[7] A. Kodama, On bimeromorphic automorphisms of hyperbolic complex spaces, Nagoya Math. J., 73 (1979), 1-5.
[8] S. Lang, Higher dimensional Diophantine problems, Bull. Amer. Math. Soc., 80 (1974), 779-787.
[9] S. Lang, Introduction to Complex Hyperbolic Spaces, Springer-Verlag, New York-Berlin-Heidelberg, 1987.
[10] Ju.I. Manin, Rational points of algebraic curves over function fields, Izv. Akad. Nauk SSSR Ser. Mat., 27 (1963), 1395-1440.
[11] T. Miyano and J. Noguchi, Moduli spaces of harmonic and holomorphic mappings and Diophantine geometry, in Prospects in Complex Geometry, Proc. 25th Taniguchi International Symposium, Katata/Kyoto, 1989, Lecture Notes in Math., 1468, Springer-Verlag, Heidelberg, 1991.
[12] J. Noguchi, Hyperbolic fibre spaces and Mordell's conjecture over function fields, Publ. Res. Inst. Math. Sci. Kyoto University, 21 (1985), 27-46.
[13] J. Noguchi, Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces, Invent. Math., 93 (1988), 15-34.
[14] J. Noguchi, Hyperbolic manifolds and Diophantine geometry, Sugaku Expositions,Amer. Math. Soc., Providence, Rhode Island, 1991. (Translation of Japanese version, Sugaku, 41 (1989), 320-334.)
[15] J. Noguchi, An example of a hyperbolic fiber space without hyperbolic embedding into compactification, Proceedings of Osaka International Conference, Osaka 1990.
[16] J. Noguchi, Meromorphic mappinngs into compact hyperbolic complex spaces and geometric Diophantine problems, Internat. J. Math., 3 (1992), 277-289, and its correction (to appear).
[17] J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, Transl. Math. Monographs., 80, Amer. Math. Soc., Providence, Rhode Island, 1990.
[18] J. Noguchi and T. Sunada, Finiteness of the family of rational and meromorphic mappings into algebraic varieties, Amer. J. Math., 104 (1982), 887-900.
[19] T. Sunada, Holomorphic mappings into a compact quotient of symmetric bounded domain, Nagoya Math. J., 64 (1976), 159-175.
[20] R. Tsushima, Rational maps to varieties of hyperbolic type, Proc. Japan Acad. Ser. A, 55 (1979), 95-100.
[21] T. Urata, Holomorphic mappings into taut complex analytic spaces, Tohoku Math. J., 31 (1979), 349-353.
[22] M. G. Zaidenberg, A function-field analog of the Mordell conjecture: A noncompact version, Math. USSR-Izv., 35 (1990), 61-81.

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