Skip to main content

Introduction to the carlson — Griffiths equidistribution theory

  • Conference paper
  • First Online:
Value Distribution Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 981))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahlfors, L. V.: The theory of meromorphic curves. Acta Soc. Sci. Fenn. Nova Ser. A 3 (4) (1941), 1–31.

    MathSciNet  MATH  Google Scholar 

  2. Biancofiore, A.: A hypersurface defect relation for a class of meromorphic maps. Trans. Amer. Math. Soc. 270 (1982), 47–60.

    Article  MathSciNet  MATH  Google Scholar 

  3. Biancofiore, A.: A defect relation for meromorphic maps. Manuscript.

    Google Scholar 

  4. Biancofiore, A., Stoll, W.: Another proof of the lemma of the logarithmic derivative in several complex variables, in "Recent developments in several complex variables". Annals of Math. Studies 100, Princeton University Press, Princeton, N.J. (1981), 29–45.

    Google Scholar 

  5. Carlson, J., Griffiths, Ph.: A defect relation for equidimensional holomorphic mappings between algebraic varieties. Ann. of Math. 95 (1972), 557–584.

    Article  MathSciNet  MATH  Google Scholar 

  6. Cartan, H.: Sur les zéros des combinaisons linéaires des p fonctions holomorphes données. Mathematica (Cluj) 7 (1933), 5–31.

    MathSciNet  MATH  Google Scholar 

  7. Chern, S. S.: The integrated form of the first main theorem for complex analytic mappings in several variables. Ann. of Math. 71 (1960), 536–551.

    Article  MathSciNet  MATH  Google Scholar 

  8. Chern, S. S.: Complex manifolds without potential theory. Van Nostrand, Princeton, N.J. (1967).

    MATH  Google Scholar 

  9. Federer, H.: Geometric measure theory. Springer-Verlag, Berlin-Heidelberg-New York (1969).

    MATH  Google Scholar 

  10. Grauert, H., Remmert, R.: Plurisubharmonische Funktionen in komplexen Räumen. Math. Z. 65 (1956), 175–194.

    Article  MathSciNet  MATH  Google Scholar 

  11. Green, M.: Some Picard theorems for holomorphic maps to algebraic varieties. Amer. J. Math. 97 (1975), 43–75.

    Article  MathSciNet  MATH  Google Scholar 

  12. Griffiths, Ph.: Holomorphic mappings into canonical algebraic varieties. Ann. of Math. 93 (1971), 439–458.

    Article  MathSciNet  MATH  Google Scholar 

  13. Griffiths, Ph.: Entire holomorphic mappings in one and several complex variables. Annals of Math. Studies 85, Princeton University Press, Princeton, N.J. (1976).

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Harvey, R.: Removable singularities for positive currents. Amer. J. Math. 96 (1974), 67–78.

    Article  MathSciNet  MATH  Google Scholar 

  16. Hayman, W. K.: Meromorphic functions. Oxford University Press, Oxford (1964).

    MATH  Google Scholar 

  17. Kobayashi, S.: Hyperbolic manifolds and holomorphic mappings. Marcel Dekker, Inc., New York (1970).

    MATH  Google Scholar 

  18. Lelong, P.: Fonctions entières (n variables) et fonctions plurisousharmoniques d'ordre fini dans ℂn. J. Analyse Math. 12 (1964), 365–407.

    Article  MathSciNet  MATH  Google Scholar 

  19. Lelong, P.: Fonctions plurisousharmoniques et forms différentielles positives. Gordon & Breach, Paris (1968)

    MATH  Google Scholar 

  20. Molzon, R. E.: Sets omitted by equidimensional holomorphic mappings. Amer. J. Math. 101 (1979), 1271–1283.

    Article  MathSciNet  MATH  Google Scholar 

  21. Molzon, R. E., Shiffman, B., Sibony, N.: Average growth estimates for hyperplane sections of entire analytic sets. Math. Ann. 257 (1981), 43–59.

    Article  MathSciNet  MATH  Google Scholar 

  22. Nevanlinna, R.: Le théorème de Picard-Borel et la théorie des fonctions méromorphes. Gauthiers-Villars, Paris (1929).

    MATH  Google Scholar 

  23. Nevanlinna, R.: Analytic functions. Springer-Verlag, Berlin-Heidelberg-New York (1970)

    Book  MATH  Google Scholar 

  24. Ochiai, T.: On holomorphic curves in algebraic varieties with ample irregularity. Invent. Math. 43 (1977), 83–96.

    Article  MathSciNet  MATH  Google Scholar 

  25. Schwartz, L.: Théorie des distributions. Hermann, Paris (1966).

    MATH  Google Scholar 

  26. Shiffman, B.: Extension of positive line bundles and meromorphic maps. Invent. Math. 15 (1972), 332–347.

    Article  MathSciNet  MATH  Google Scholar 

  27. Shiffman, B.: Nevanlinna defect relations for singular divisors. Invent. Math. 31 (1975), 155–182.

    Article  MathSciNet  MATH  Google Scholar 

  28. Shiffman, B.: Holomorphic curves in algebraic manifolds. Bull. Amer. Math. Soc. 83 (1977), 553–568.

    Article  MathSciNet  MATH  Google Scholar 

  29. Shiffman, B.: On holomorphic curves and meromorphic maps in projective space. Indiana Univ. Math. J. 28 (1979), 627–641.

    Article  MathSciNet  MATH  Google Scholar 

  30. Shiffman, B.: A general second main theorem for meromorphic functions on ℂn. To appear in Amer. J. Math.

    Google Scholar 

  31. Stoll, W.: Die beiden Hauptsätze der Wertverteilungstheorie bei Funktionen mehrerer komplexen Veränderlichen I, II. Acta Math. 90 (1953), 1–115, 92 (1954), 55–169.

    Article  MathSciNet  MATH  Google Scholar 

  32. Stoll, W.: About value distribution of holomorphic maps into projective space. Acta Math. 123 (1969), 83–114.

    Article  MathSciNet  MATH  Google Scholar 

  33. Stoll, W.: Value distribution of holomorphic maps into compact complex manifolds. Lecture Notes in Mathematics 135, Springer-Verlag, Berlin-Heidelberg-New York (1970).

    MATH  Google Scholar 

  34. Stoll, W.: Value distribution of parabolic spaces. Lecture Notes in Mathematics 600, Springer-Verlag, Berlin-Heidelberg-New York (1977).

    Book  MATH  Google Scholar 

  35. Stolzenberg, G.: Volumes, limits, and extensions of analytic varieties. Lecture Notes in Mathematics 19, Springer-Verlag, Berlin-New York (1966).

    MATH  Google Scholar 

  36. Vitter, A.: The lemma of the logarithmic derivative in several complex variables. Duke Math. J. 44 (1977), 89–104.

    Article  MathSciNet  MATH  Google Scholar 

  37. Wells, R. O.: Differential analysis on complex manifolds. Prentice-Hall, Englewood Cliffs, N.J. (1973).

    MATH  Google Scholar 

  38. Weyl, H., Weyl, J.: Meromorphic functions and analytic curves. Annals of Math. Studies 12, Princeton University Press, Princeton, N.J. (1943).

    MATH  Google Scholar 

  39. Wu, H.: The equidistribution theory of holomorphic curves. Annals of Math. Studies 64, Princeton University Press, Princeton, N.J. (1970).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ilpo Laine Seppo Rickman

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Shiffman, B. (1983). Introduction to the carlson — Griffiths equidistribution theory. In: Laine, I., Rickman, S. (eds) Value Distribution Theory. Lecture Notes in Mathematics, vol 981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066383

Download citation

  • DOI: https://doi.org/10.1007/BFb0066383

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12003-2

  • Online ISBN: 978-3-540-39480-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics