Value Distribution Theory and Related Topics pp 281-319 | Cite as
Jet Bundles and its Applications in Value Distribution of Holomorphic Mappings
Chapter
Abstract
In this paper, we have established the technique of the higher dimensional jets and applied the results to study value distribution of holomorphic mappings. As applications, we have also generalized the results of holomorphic curves obtained by Ochiai, Noguchi and Green-Griffiths to the higher dimensional cases.
Key words and phrases
jet bundle holomorphic mapping Nevanlinna theoryMathematics Subject Classification 2000
32A22 32H30Preview
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References
- 1.Biancofiore, A. and Stoll, W., Another proof of the lemma of the logarithmic derivative in several complex variables, Ann. of Math. Stud., 100, pp. 29–45, Princeton University Press, Princeton, N.J., 1981.Google Scholar
- 2.Bloch, A., Sur les systèms de fonctions uniformes satisfaisant à l’équation d’une variété algébrique dont l’irrégularité dépasse la dimension, J. Math. Pure Appl. 5 (1926), 19–66.MATHGoogle Scholar
- 3.Bogomolov, F., Families of curves on a surface of general type, Soviet Math. Dokl. 236 (1977), 1294–1297.MATHMathSciNetGoogle Scholar
- 4.Deligne, P., Equations différentielles à points singuliers réguliers, Lecture Notes in Math., 163, Springer-Verlag, Berlin, 1970.Google Scholar
- 5.Dolgachev, I., Weighted projective varieties, Group actions and vector fields (Vancouver, B.C., 1981), 34–71, Lecture Notes in Math., 956, Springer, Berlin, 1982.Google Scholar
- 6.Green, M. and Griffiths, P., Two applications of algebraic geometry to entire holomorphic mappings, The Chern Symposium 1979 (Proc. Internat. Sympos., Berkeley, Calif., 1979), pp. 41–74, Springer, New York-Berlin, 1980.Google Scholar
- 7.Griffiths, P. and King, J., Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math. 130 (1973), 145–220.MathSciNetGoogle Scholar
- 8.Iitaka, S., Logarithmic forms of algebraic varieties, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), 525–544.MATHMathSciNetGoogle Scholar
- 9.Kawamata, Y., On Bloch’s conjecture, Invent. Math. 57 (1980), 97–100.CrossRefMATHMathSciNetGoogle Scholar
- 10.Lang, S., Hyperbolic and Diophantine analysis, Bull. Amer. Math. Soc. (N.S.) 14 (1986), no.2, 159–205.MATHMathSciNetGoogle Scholar
- 11.Lang, S. and Cherry, W., Topics in Nevanlinna Theory, Lecture Notes in Math., 1433, Springer Verlag, 1990.Google Scholar
- 12.Noguchi, J., Holomorphic curves in algebraic varieties, Hiroshima Math. J. 7 (1977), 833–853.MATHMathSciNetGoogle Scholar
- 13.Noguchi, J., Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties, Nagoya Math. J. 83 (1981), 213–233.MATHMathSciNetGoogle Scholar
- 14.Noguchi, J. and Ochiai, T., Geometric Function Theory in Several Variables, Translations of Mathematical Monographs, 80, AMS, Providence, 1990.Google Scholar
- 15.Ochiai, T., On holomorphic curves in algebraic varieties with ample irregularity, Invent. Math. 43 (1977), 83–96.CrossRefMATHMathSciNetGoogle Scholar
- 16.Smyth, B., Weakly ample Kähler manifolds and Euler numbers, Math. Ann. 224 (1976), 269–279.CrossRefMATHMathSciNetGoogle Scholar
- 17.Stoll, W., Value distribution on parabolic spaces, Lecture Notes in Math., 600, Springer-Verlag, Berlin-New York, 1977.Google Scholar
- 18.Ueno, K., Classification of algebraic varieties I, Compositio Math. 27 (1973), 277–342.MATHMathSciNetGoogle Scholar
- 19.Vitter, A., The lemma of the logarithmic derivative in several complex variables, Duke Math. J. 44 (1977), 89–104.CrossRefMATHMathSciNetGoogle Scholar
- 20.Weil, A., Introduction à l’étude des variétés kählériennes, (French) Publications de l’Institut de Mathmatique de l’Universit de Nancago, VI. Actualits Sci. Ind. no. 1267 Hermann, Paris 1958.Google Scholar
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