Skip to main content

Moduli spaces of harmonic and holomorphic mappings and diophantine geometry

Part of the Lecture Notes in Mathematics book series (LNM,volume 1468)

Keywords

  • Modulus Space
  • Holomorphic Mapping
  • Abelian Variety
  • Isometric Immersion
  • Hodge Structure

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S.Ju. Arakelov, Families of algebraic curves with fixed degeneracies, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 1277–1302.

    MathSciNet  MATH  Google Scholar 

  2. R. Brody, Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc. 235 (1978), 213–219.

    MathSciNet  MATH  Google Scholar 

  3. A. Borel and R. Narasimhan, Uniqueness conditions for certain holomorphic mappings, Invent. Math. 2 (1967), 247–255.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. G. Faltings, Arakelov's theorem for Abelian varieties, Invent. Math. 73 (1983), 337–347.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349–366.

    CrossRef  MathSciNet  Google Scholar 

  6. G. Faltings, Diophantine approximation on Abelian varieties, preprint.

    Google Scholar 

  7. H. Grauert, Mordells Vermutung über rationale Punkte auf Algebraischen Kurven und Funktionenkörper, Publ. Math. IHES 25 (1965), 131–149.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. P. Griffiths and J. King, Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math. 130 (1973), 145–220.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. M. Green, Holomorphic maps to complex tori, Amer. J. Math. 100 (1978), 615–620.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. C. Horst, Compact varieties of surjective holomorphic mappings, Math. Z. 196 (1987), 259–269.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. C. Horst, A finiteness criterion for compact varieties of surjective holomorphic mappings, preprint.

    Google Scholar 

  12. Y. Imayoshi, Generalizations of de Franchis theorem, Duke Math. J. 50 (1983), 393–408.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Y. Imayoshi and H. Shiga, A finiteness theorem for holomorphic families of Riemann surfaces. Holomorphic Functions and Moduli II, pp. 207–219, Springer-Verlag, New York-Berlin, 1988.

    CrossRef  MATH  Google Scholar 

  14. S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York 1970.

    MATH  Google Scholar 

  15. S. Kobayashi, Negative vector bundles and complex Finsler structures, Nagoya Math. J. 57 (1975), 153–166.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. S. Kobayashi, Intrinsic distances, measures, and geometric function theory, Bull. Amer. Math. Soc. 82 (1976), 357–416.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. S. Kobayashi and T. Ochiai, Satake compactification and the great Picard theorem, J. Math. Soc. Japan 23 (1971), 340–350.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. S. Kobayashi and T. Ochiai, Meromorphic mappings onto compact complex spaces of general type, Invent. Math. 31 (1975), 7–16.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. M. Kalka, B. Schiffman and B. Wang, Finiteness and rigidity theorems for holomorphic mappings, Michigan Math. J. 28 (1981), 289–295.

    CrossRef  MathSciNet  Google Scholar 

  20. S. Lang, Higher dimensional Diophantine problems, Bull. Amer. Math. Soc. 80 (1974), 779–787.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. S. Lang, Fundamentals of Diophantine Geometry, Springer-Verlag, Berlin, 1983.

    CrossRef  MATH  Google Scholar 

  22. S. Lang, Hyperbolic and Diophantine analysis, Bull. Amer. Math. Soc., 14 (1986), 159–205.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. Ju. Manin, Rational points of algebraic curves over function fields, Izv. Akad. Nauk. SSSR. Ser. Mat. 27 (1963), 1395–1440.

    MathSciNet  MATH  Google Scholar 

  24. S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. Math. 116 (1982), 133–176.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. S. Mori and S. Mukai, The uniruledness of the moduli space of curves of genus 11, Algebraic Geometry, Proc. Japan-France Conf. Tokyo and Kyoto 1982, Lecture Notes in Math. 1016, Springer-Verlag, Berlin-Heidelberg-New York, 1983.

    MATH  Google Scholar 

  26. J. Noguchi, A higher dimensional analogue of Mordell's conjecture over function fields, Math. Ann. 258 (1981), 207–212.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. J. Noguchi, Hyperbolic fibre spaces and Mordell's conjecture over function fields, Publ. RIMS, Kyto University 21 (1985), 27–46.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. J. Noguchi, Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces, Invent. Math. 93 (1988), 15–34.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, to appear from A.M.S. Monograph Series (the Japanese edition, Iwanami Shoten, Tokyo, 1984).

    Google Scholar 

  30. J. Noguchi and T. Sunada, Finiteness of the family of rational and meromorphic mappings into algebraic varieties, Amer. J. Math. 104 (1982), 887–900.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. A.N. Parshin, Algebraic curves over function fields, I, Izv. Akad. Nauk SSSR Ser. Mat., 32 (1968), 1145–1170.

    MathSciNet  MATH  Google Scholar 

  32. A.N. Parshin, Finiteness theorems and hyperbolic manifolds, preprint.

    Google Scholar 

  33. C. Peters, Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems, Compositio Math.

    Google Scholar 

  34. M. Raynoud, Around the Mordell conjecture for function fields and a conjecture of Serge Lang, Lecture Notes in Math., vol. 1016, pp. 1–19, Springer-Verlag, Berlin-New York, 1983.

    Google Scholar 

  35. H.L. Royden, Automorphisms and isometries of Teichmüller spaces, Advances in the Theory of Riemann Surfaces, pp. 369–383, Ann. of Math. Studies 66, Princeton Univ. Press, Princeton, New Jersey, 1971.

    Google Scholar 

  36. M.-H. Saito and S. Zucker, Classification of non-rigid families of K3 surfaces and a finiteness theorem of Arakelov type, preprint.

    Google Scholar 

  37. R. Schoen and S.-T. Yau, Compact group actions and the topology of manifolds with non-positive curvature, Topology 18 (1979), 361–380.

    CrossRef  MathSciNet  MATH  Google Scholar 

  38. T. Sunada, Holomorphic mappings into a compact quotient of symmetric bounded domain, Nagoya Math. J. 64 (1976), 159–175.

    CrossRef  MathSciNet  MATH  Google Scholar 

  39. T. Sunada, Rigidity of certain harmonic mappings, Invent. Math. 51 (1979), 297–307.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Miyano, T., Noguchi, J. (1991). Moduli spaces of harmonic and holomorphic mappings and diophantine geometry. In: Noguchi, J., Ohsawa, T. (eds) Prospects in Complex Geometry. Lecture Notes in Mathematics, vol 1468. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086196

Download citation

  • DOI: https://doi.org/10.1007/BFb0086196

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54053-3

  • Online ISBN: 978-3-540-47370-1

  • eBook Packages: Springer Book Archive