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The currents defined by analytic varieties

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Acta Mathematica

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References

  1. Abhyankar, S. S.,Local analytic geometry. Academic Press, New York 1964.

    MATH  Google Scholar 

  2. Almgren, F. J., Jr., Measure theoretic geometry and elliptic variational problems.Bull. Amer. Math. Soc., 75 (1968), 285–304.

    Article  MathSciNet  Google Scholar 

  3. Andreotti, A. &Norguet, F., La convexité holomorphe dans l'espace analytique des cycles d'une variété algébrique.Ann. Scuola Norm. Pisa, 21 (1967), 31–82.

    MathSciNet  MATH  Google Scholar 

  4. Bloom, T. &Herrera, M., De Rham cohomology of an analytic space.Invent. Math., 7 (1969), 275–296.

    Article  MathSciNet  Google Scholar 

  5. Borel, A. &Haefliger, A., La classe d'homologie fondamentale d'un espace analytique.Bull. Soc. Math. France., 89 (1961), 461–513.

    MathSciNet  MATH  Google Scholar 

  6. Draper, R. N., Intersection theory in analytic geometry.Math. Ann., 180 (1969), 175–204.

    Article  MATH  MathSciNet  Google Scholar 

  7. Federer, H.,Geometric measure theory. Springer-Verlag, New York, 1969.

    MATH  Google Scholar 

  8. —, Some theorems on integral currents,Trans. Amer. Math. Soc., 117 (1965), 43–67.

    Article  MATH  MathSciNet  Google Scholar 

  9. Gunning, R. C. &Rossi, H.,Analytic functions of several complex variables. Prentice-Hall, Englewood Cliffs, N.J. 1965.

    MATH  Google Scholar 

  10. Hurewicz, W. & Wallman, H.,Dimension theory. Princeton, 1941.

  11. King, J., Families of intermediate jacobians. Thesis (Berkeley, 1969).

  12. Lelong, P., Fonctions plurisousharmoniques ...Colloque sur les fonctions de plusieurs variables, Bruxelles. Masson, Paris, 1953.

    Google Scholar 

  13. —, Intégration sur un ensemble analytique complexe,Bull. Soc. Math. France., 85 (1957), 239–262.

    MATH  MathSciNet  Google Scholar 

  14. Lelong, P., Propriétés métriques des ensembles analytiques complexes.Seminaire Lelong, 1965/66 no. 2. Paris 1966.

  15. de Rham, G.,Variétés différentiables. Hermann, Paris, 1960.

    MATH  Google Scholar 

  16. —, Currents in an analytic complex manifold.Seminar on analytic functions, Vol. I. Institute for Advanced Study, Princeton, 1957.

    Google Scholar 

  17. Saks, S.,Theory of the integral. Dover, New York, 1964.

    Google Scholar 

  18. Schwartz, L.,Théorie des distributions. Hermann. Paris, (New edition), 1966.

    MATH  Google Scholar 

  19. Shiffman, B., On the removal of singularities of analytic sets,Mich. Math. J., 15 (1968), 111–120.

    Article  MATH  MathSciNet  Google Scholar 

  20. —, On the continuation of analytic curves.Math. Ann., 184 (1970), 268–274.

    Article  MATH  MathSciNet  Google Scholar 

  21. —, On the continuation of analytic sets.Math Ann., 185 (1970), 1–12.

    Article  MATH  MathSciNet  Google Scholar 

  22. Stoll, W., The multiplicity of a holomorphic map.Invent. Math., 2 (1966), 15–58.

    Article  MATH  MathSciNet  Google Scholar 

  23. —, The continuity of the fiber integral.Math. Z., 95 (1967), 87–138.

    Article  MATH  MathSciNet  Google Scholar 

  24. —, The fiber integral is constant.Math. Z., 104 (1968), 65–73.

    Article  MATH  MathSciNet  Google Scholar 

  25. Stolzenberg, G.,Volumes, limits, and extensions of analytic varieties. Springer-Verlag, New York, 1966.

    MATH  Google Scholar 

  26. Thie, P., The Lelong number of a point of a complex analytic set,Math. Ann., 172 (1967), 269–312.

    Article  MATH  MathSciNet  Google Scholar 

  27. Van der Waerden, B. L.,Modern algebra Vol. I. Ungar, New York, 1953.

    Google Scholar 

  28. Weil, A.,Variétés Kählérienes. Hermann, Paris, 1958.

    Google Scholar 

  29. Whitney, H., Tangents to an analytic variety,Ann. of Math., 81 (1965), 496–549.

    Article  MATH  MathSciNet  Google Scholar 

Added in proof

  1. Bombieri, E., Algebraic values of meromorphic maps,Invent. Math., 10 (1970), 267–287.

    Article  MATH  MathSciNet  Google Scholar 

  2. —, Addendum to my paper “Algebraic values of meromorphic maps”Invent. Math., 11 (1970), 163–166.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, Mass., USA

    James R. King

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  1. James R. King
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This research supported in part by an NSF Graduate Fellowship and NSF Grant GP 13876 13-712907Acta mathematica 127. Imprimé le 8 Octobre 1971

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King, J.R. The currents defined by analytic varieties. Acta Math. 127, 185–220 (1971). https://doi.org/10.1007/BF02392053

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  • DOI: https://doi.org/10.1007/BF02392053

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