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

Makoto SUZUKI

doi:10.2969/jmsj/04640681

Makoto SUZUKI

著者情報

ジャーナルフリー

1994 年 46 巻 4 号 p. 681-698

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

詳細

Published: 1994 Received: 1992/10/26 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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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