Inventiones mathematicae

, Volume 93, Issue 1, pp 15–34 | Cite as

Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces

  • Junjiro Noguchi


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  1. 1.
    Arakelov, S.Ju.: Families of algebraic curves with fixed degeneracies. Izv. Akad. Nauk SSSR, Ser. Mat.35, 1277–1302 (1971)Google Scholar
  2. 2.
    Borel, A.: Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem. J. Differ. Geom.6, 543–560 (1972)Google Scholar
  3. 3.
    Douady, A.: Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné. Ann. Inst. Fourier, Grenoble16, 1–95 (1966)Google Scholar
  4. 4.
    Eells, J., Lemaire, L.: Selected topics in harmonic maps. CBMS, Amer. Math. Soc.50 (1983)Google Scholar
  5. 5.
    Faltings, G.: Arakelov's theorem for Abelian varieties. Invent. Math.73, 337–347 (1983)Google Scholar
  6. 6.
    Frisch, J.: Points de platitude d'un morphisme d'espaces analytiques complexes. Invent. Math.4, 118–138 (1967)Google Scholar
  7. 7.
    Fujiki, A.: Closedness of the Douady spaces of compact Kähler spaces. Publ. RIMS, Kyoto Univ.14, 1–52 (1978)Google Scholar
  8. 8.
    Griffiths, P., King, J.: Nevanlinna theory and holomorphic mappings between algebraic varieties. Acta Math.130, 145–220 (1973)Google Scholar
  9. 9.
    Hironaka, H.: Flattening theorem in complex-analytic geometry. Am. J. Math.97, 503–547 (1975)Google Scholar
  10. 10.
    Imayoshi, Y.: Generalizations of de Franchis theorem. Duke Math. J.50, 393–408 (1983)Google Scholar
  11. 11.
    Imayoshi, Y., Shiga, H.: A finiteness theorem for holomorphic families of Riemann surfaces, to appear in Proc. Holomorphic Functions and Moduli, MSRI Berkeley, 1986Google Scholar
  12. 12.
    Kiernan, P.: Extensions of holomorphic maps. Trans. Am. Math. Soc.172, 347–355 (1972)Google Scholar
  13. 13.
    Kiernan, P., Kobayashi, S.: Holomorphic mappings into projective space with lacunary hyperplanes. Nagoya Math. J.50, 199–216 (1973)Google Scholar
  14. 14.
    Kiernan, P.: On the compactifications of arithmetic quotients of symmetric spaces. Bull. Am. Math. Soc.80, 109–110 (1974)Google Scholar
  15. 15.
    Kiernan, P., Kobayashi, S.: Comments on Satake compactification and the great Picard theorem. J. Math. Soc. Japan28, 577–580 (1976)Google Scholar
  16. 16.
    Kobayashi, S.: Hyperbolic manifolds and holomorphic mappings. New York: Marcel Dekker 1970Google Scholar
  17. 17.
    Kobayashi, S., Ochiai, T.: Satake compactification and the great Picard theorem. J. Math. Soc. Japan23, 340–350 (1971)Google Scholar
  18. 18.
    Kobayashi, S., Ochiai, T.: Meromorphic mappings onto compact complex spaces of general type. Invent. Math.31, 7–16 (1975)Google Scholar
  19. 19.
    Kobayashi, S.: Intrinsic distances, measures, and geometric function theory. Bull. Am. Math. Soc.82, 357–416 (1976)Google Scholar
  20. 20.
    Kuga, M., Ihara, S.-I.: Family of families of Abelian varieties. Algebriac Number Theory, Kyoto, 1976, pp. 126–142. Tokyo: Japan Soc. for the Promotion of Science, 1977Google Scholar
  21. 21.
    Kwack, M.H.: Generalization of the big Picard theorem. Ann. Math.90, 9–22 (1969)Google Scholar
  22. 22.
    Margulis, G.A.: Arithmeticity of non-uniform lattices. Funct. Anal. Appl.7, 245–246 (1973)Google Scholar
  23. 23.
    Mumford, D.: Curves and their Jacobians. Ann Arbor: Univ. of Michigan Press, 1975Google Scholar
  24. 24.
    Noguchi, J., Sunada, T.: Finiteness of the family of rational and meromorphic mappings into algebraic varieties. Am. J. Math.104, 887–900 (1982)Google Scholar
  25. 25.
    Noguchi, J.: Logarithmic jet spaces and extensions of de Franchis' theorem. Contributions to several complex variables. Aspects Math. E9, pp. 227–249. Braunschweig: Vieweg, 1986Google Scholar
  26. 26.
    Parshin, A.N.: Algebraic curves over function fields. I, Izv. Akad. Nauk SSSR, Ser. Mat.32, 1145–1170 (1968)Google Scholar
  27. 27.
    Satake, I.: On numerical invartiants of arithmetic varieties ofQ-rank one. Automorphic forms of several variables, Taniguchi Symposium, Katata. 1983, pp. 353–369. Boston: Birkhäuser 1984Google Scholar
  28. 28.
    Schoen, R., Yau, S.T.: Compact group actions and the topology of manifolds with non-positive curvature. Topology18, 361–380 (1979)Google Scholar
  29. 29.
    Stolzenberg, G.: Volumes, limits, and extensions of analytic varieties. (Lect. Notes Math., Vol. 19). Berlin-Heidelberg-New York: Springer 1966Google Scholar
  30. 30.
    Sunada, T.: Holomorphic mappings into a compact quotient of symmetric bounded domain. Nagoya Math. J.64, 159–175 (1976)Google Scholar
  31. 31.
    Sunada, T.: Rigidity of certain harmonic mappings. Invent. Math.51, 297–307 (1979)Google Scholar
  32. 32.
    Tsushima, R.: Rational maps to varieties of hyperbolic type. Proc. Japan Acad.55, 95–100 (1979)Google Scholar
  33. 33.
    Urata, T.: The hyperbolicity of complex analytic spaces. Bull. Aichi Univ. of Education (Natural Scie.)XXXI, 65–75 (1982)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Junjiro Noguchi
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceTokyo Institute of TechnologyTokyoJapan

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