References
Ahlfors, L. V., The theory of meromorphic curves.Acta Soc. Sci. Fennicae Nova Ser. A., 3:4 (1941), 1–31.
Aihara, Y. &Noguchi, J., Value distribution of meromorphic mappings into compactified locally symmetric spaces.Kodai Math. J., 14 (1991), 320–334.
Ax, J., Some topics in differential algebraic geometry, II,Amer. J. Math., 94 (1972), 1205–1213.
Bloch, A., Sur les systèmes de fonctions uniformes satisfaisant à l'équation d'une variété algébrique dont l'irrégularité dépasse la dimension.J. Math. Pures Appl. (9), 5 (1926), 19–66.
Brody, R., Compact manifolds and hyperbolicity.Trans. Amer. Math. Soc., 235 (1978), 213–219.
Cartan, H., Sur les zéros des combinaisons linéaires dep fonctions holomorphes données.Mathematica (Cluj), 7 (1933), 5–31.
Carlson, J. &Griffiths, P., A defect relation for equidimensional holomorphic mappings between algebraic varieties.Ann. of Math. (2), 95 (1972), 557–584.
Dethloff, G.-E. &Lu, S. S.-Y., Logarithmic jet bundles and applications.Osaka J. Math., 38 (2001), 185–237.
Eremenko, A. E. &Sodin, M. L., The value distribution of meromorphic functions and meromorphic curves from the point of view of potential theory.Algebra i Analiz, 3 (1991), 131–164; English translation inSt. Petersburg Math. J., 3 (1992), 109–136.
Griffiths, P. &King, J., Nevanlinna theory and holomorphic mappings between algebraic varieties.Acta Math., 130 (1973), 145–220.
Grant, C. G., Entire holomorphic curves in surfaces.Duke Math. J., 53 (1986), 345–358.
Hayman, W. K.,Meromorphic Functions. Oxford Math. Monographs. Clarendon Press, London, 1964.
Kawamata, Y., On Bloch's conjecture.Invent. Math., 57 (1980), 97–100.
Kobayashi, R., Holomorphic curves into algebraic subvarieties of an abelian variety.Internat. J. Math., 2 (1991), 711–724.
—, Holomorphic curves in abelian varieties: the second main theorem and applications.Japan. J. Math. (N.S.), 26 (2000), 129–152.
Kobayashi, S.,Hyperbolic Complex Spaces. Grundlehren Math. Wiss., 318. Springer-Verlag, Berlin, 1998.
Lang, S.,Introduction to Complex Hyperbolic Spaces. Springer-Verlag, New York, 1987.
McQuillan, M., A dynamical counterpart to Faltings' “Diophantine approximation on Abelian varieties”. Preprint, I.H.E.S., 1996.
Noguchi, J., Holomorphic curves in algebraic varieties.Hiroshima Math. J., 7 (1977), 833–853.
—, Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties.Nagoya Math. J., 83 (1981), 213–233.
—, Logarithmic jet spaces and extensions of de Franchis' theorem, inContributions to Several Complex Variables, pp. 227–249. Aspects Math., E9, Vieweg, Braunschweig, 1986.
—, On Nevanlinna's second main theorem, inGeometric Complex Analysis (Hayama, 1995), pp. 489–503. World Sci. Publishing, Singapore, 1996.
—, On holomorphic curves in semi-Abelian varieties.Math. Z., 228 (1998), 713–721.
Noguchi, J. &Ochiai, T.,Geometric Function Theory in Several Complex Variables. Japanese edition: Iwanami, Tokyo, 1984; English translation: Transl. Math. Monographs, 80. Amer. Math. Soc., Providence, RI, 1990.
Noguchi, J. & Winkelmann, J., Holomorphic curves and integral points off divisors. To appear inMath. Z.
Noguchi, J., Winkelmann, J. &Yamanoi, K., The value distribution of holomorphic curves into semi-Abelian varieties.C. R. Acad. Sci. Paris Sér. I Math., 331 (2000), 235–240.
Siu, Y.-T., Defect relations for holomorphic maps between spaces of different dimensions.Duke Math. J., 55 (1987), 213–251.
Stoll, W., Die beiden Hauptsätze der Wertverteilungstheorie bei Funktionen mehrerer komplexer Veränderlichen, I; II.Acta Math., 90 (1953), 1–115;Ibid.,Stoll, W., Die beiden Hauptsätze der Wertverteilungstheorie bei Funktionen mehrerer komplexer Veränderlichen, I; II.Acta Math., 92 (1954), 55–169.
Siu, Y.-T. &Yeung, S.-K., A generalized Bloch's theorem and the hyperbolicity of the complement of an ample divisor in an Abelian variety.Math. Ann., 306 (1996), 743–758.
—, Defects for ample divisors of Abelian varieties, Schwarz lemma, and hyperbolic hypersurfaces of low degrees.Amer. J. Math., 119 (1997), 1139–1172.
Weil, A.,Introduction à l'étude des variétés kählériennes. Hermann, Paris, 1958.
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Research supported in part by Grant-in-Aid for Scientific Research (A)(1), 13304009.
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Noguchi, J., Winkelmann, J. & Yamanoi, K. The second main theorem for holomorphic curves into semi-Abelian varieties. Acta Math. 188, 129–161 (2002). https://doi.org/10.1007/BF02392797
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DOI: https://doi.org/10.1007/BF02392797