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Holomorphic mapping into algebraic varieties of general type

Published online by Cambridge University Press:  22 January 2016

Peichu Hu*
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong, China
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We will study holomorphic mappings

from a connected complex manifold M of dimension m to a projective algebraic manifold N of dimension n. Assume first that N is of general type, i.e.

where KNN is the canonical bundle of N. If KN is positive, then N is of general type.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[1] Chern, S. S., Shiing-Shen Chern selected papers, Springer-Verlag New York Heidelberg Berlin, 347360.Google Scholar
[2] Griffiths, Ph., Holomorphic mapping into canonical algebraic varieties, Ann. of Math., (2) 93 (1971), 439458.Google Scholar
[3] Griffiths, Ph. and King, J., Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta. Math., 130 (1973), 145220.CrossRefGoogle Scholar
[4] Hu, P. C., On Griffiths’ Conjecture in value distribution of holomorphic maps, to appear.Google Scholar
[5] Kobayashi, S. and Ochiai, T., Mappings into compact complex manifolds with negative Chern class, J. Math. Soc. Japan, 23 (1971), 137148.Google Scholar
[6] Kodaira, K., On holomorphic mappings of polydiscs into compact complex manifolds, J. Diff. Geom., 6 (1971), 3346.Google Scholar
[7] Nevanlinna, R., Eindeutige analytische Funktionen. Die Grundl., d. Math. Wiss. XLVC Springer Verlag. Berlin-Göttingen-Heidelberg 2 ed. 1953.Google Scholar
[8] Stoll, W., Value distribution on parabolic spaces. Lecture Notes in Mathematics 600 Springer-Verlag, Berlin-Heidelberg-New York. 1977.Google Scholar
[9] Stoll, W., Value distribution theory for meromorphic maps. Aspects of Mathematics, Vieweg. 1985.Google Scholar