Holomorphic maps of projective algebraic manifolds into compact C-hyperbolic manifolds

Yoichi IMAYOSHI

doi:10.2969/jmsj/04620289

Yoichi IMAYOSHI

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JOURNAL FREE ACCESS

1994 Volume 46 Issue 2 Pages 289-307

DOI https://doi.org/10.2969/jmsj/04620289

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Published: 1994 Received: October 15, 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: SUBTITLE Details: Wrong : Dedicated to Professor Nobuyuki Suita on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. Borel and R. Narasimhan, Uniqueness conditions for certain holomorphic mappings, Invent. Math., 2 (1967), 247-255.
2) 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.
3) D. Eisenmann, Holomorphic mappings into tight manifolds, Bull. Amer. Math. Soc., 76 (1970), 46-48.
4) H. Grauert and R. Remmert, Theory of Stein Spaces, Springer-Verlag, Berlin, Heiderberg, New York, 1979.
5) P. A. Grifiths and J. Harris, Principles of Algebraic Geometry, John Wiley, New York, 1978.
6) Y. Imayoshi, Generalizations of de Franchis theorem, Duke Math. J., 50 (1983), 393-408.
7) Y. lmayoshi, Universal covering spaces of certain quasi-projective algebraic surfaces, Osaka J. Math., 20 (1983), 581-598.
8) Y. Imayoshi, Holomorphic maps of compact Riemann surfaces into 2-dimensional compact C-hyperbolic manifolds, Math. Ann., 270 (1985), 403-416.
9) M. Kalka, B. Shiffman and B. Wong, Finiteness and rigidity theorems for holomorphic mappings, Michigan Math. J., 28 (1981), 289-295.
10) A. Kas, On deformation of a certain irregular algebraic surfaces, Amer. J. Math., 90 (1968), 789-804.
11) P. J. Kiernan, On the relations between taut, tight and hyperbolic manifolds, Bull. Amer. Math. Soc., 76 (1970), 49-51.
12) S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Dekker, New York, 1970.
13) S. Kobayashi and T. Ochiai, Meromorphic mappings onto compact complex spaces of general type, Invent. Math., 31 (1975), 7-16.
14) K. Kodaira, A certain type of irregular algebraic surfaces, J. Analyse Math., 19 (1967), 207-215.
15) K. Lamotke, The topology of complex projective varieties after S. Lefschetz, Topology, 20 (1981), 15-51.
16) J. Milnor, Morse Theory, Princeton Univ. Press, New Jersey, 1963.
17) R. Narasimhan, Several Complex Variables, The University of Chicago Press, Chicago, 1971.
18) J. Noguchi, Moduli spaces of holomorphic mappings into hyperbolically embedded complex spaces, Invent. Math., 93 (1988), 15-34.
19) J. Noguchi and T. Sunada, Finiteness of the family of rational and meromorphic mappings into algebraic varieties, Amer. J. Math., 104 (1982), 887-900.
20) T. Urata, Holomorphic mappings onto a certain complex analytic space, Tohoku Math. J., 33 (1981), 73-585.
21) H. Whitney, Complex Analytic Varieties, Addison-Wesley, Reading, Massachusetts, 1972.
22) M. G. Zaidenberg and V. Ya Lin, Finiteness theorems for holomorphic maps, in Several Complex Variables III, (ed. G.M. Khenkin), Encyclopaedia of Mathematical Sciences, 9, Springer-Verlag, 1989, pp.113-172.

Right : [1] A. Borel and R. Narasimhan, Uniqueness conditions for certain holomorphic mappings, Invent. Math., 2 (1967), 247-255.
[2] 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.
[3] D. Eisenmann, Holomorphic mappings into tight manifolds, Bull. Amer. Math. Soc., 76 (1970), 46-48.
[4] H. Grauert and R. Remmert, Theory of Stein Spaces, Springer-Verlag, Berlin, Heiderberg, New York, 1979.
[5] P. A. Grifiths and J. Harris, Principles of Algebraic Geometry, John Wiley, New York, 1978.
[6] Y. Imayoshi, Generalizations of de Franchis theorem, Duke Math. J., 50 (1983), 393-408.
[7] Y. lmayoshi, Universal covering spaces of certain quasi-projective algebraic surfaces, Osaka J. Math., 20 (1983), 581-598.
[8] Y. Imayoshi, Holomorphic maps of compact Riemann surfaces into 2-dimensional compact C-hyperbolic manifolds, Math. Ann., 270 (1985), 403-416.
[9] M. Kalka, B. Shiffman and B. Wong, Finiteness and rigidity theorems for holomorphic mappings, Michigan Math. J., 28 (1981), 289-295.
[10] A. Kas, On deformation of a certain irregular algebraic surfaces, Amer. J. Math., 90 (1968), 789-804.
[11] P. J. Kiernan, On the relations between taut, tight and hyperbolic manifolds, Bull. Amer. Math. Soc., 76 (1970), 49-51.
[12] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Dekker, New York, 1970.
[13] S. Kobayashi and T. Ochiai, Meromorphic mappings onto compact complex spaces of general type, Invent. Math., 31 (1975), 7-16.
[14] K. Kodaira, A certain type of irregular algebraic surfaces, J. Analyse Math., 19 (1967), 207-215.
[15] K. Lamotke, The topology of complex projective varieties after S. Lefschetz, Topology, 20 (1981), 15-51.
[16] J. Milnor, Morse Theory, Princeton Univ. Press, New Jersey, 1963.
[17] R. Narasimhan, Several Complex Variables, The University of Chicago Press, Chicago, 1971.
[18] J. Noguchi, Moduli spaces of holomorphic mappings into hyperbolically embedded complex spaces, Invent. Math., 93 (1988), 15-34.
[19] J. Noguchi and T. Sunada, Finiteness of the family of rational and meromorphic mappings into algebraic varieties, Amer. J. Math., 104 (1982), 887-900.
[20] T. Urata, Holomorphic mappings onto a certain complex analytic space, Tôhoku Math. J., 33 (1981), 73-585.
[21] H. Whitney, Complex Analytic Varieties, Addison-Wesley, Reading, Massachusetts, 1972.
[22] M. G. Zaidenberg and V. Ya Lin, Finiteness theorems for holomorphic maps, in Several Complex Variables III, (ed. G. M. Khenkin), Encyclopaedia of Mathematical Sciences, 9, Springer-Verlag, 1989, pp. 113-172.

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