Skip to main content
SpringerLink
Log in

Separate algebraicity along families of algebraic curves

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

A classical theorem on algebraicity in separate variables is generalized and proved.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. V. Shabat,Introduction to Complex Analysis [in Russian], Nauka, Moscow (1960).

    Google Scholar 

  2. S. Bochner and W. T. Martin,Several Complex Variables, Princeton Univ. Press, Princeton (1948).

    MATH  Google Scholar 

  3. A. B. Sukhov, “OnCR mappings of real quadric manifolds,”Michigan Math. J.,41, 143–150 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. B. Sukhov, “On the mapping problem for quadric Cauchy-Riemann manifolds,”Indiana Univ. Math. J.,42, 27–36 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Poincaré, “Les fonctions analytiques de deux variables et la représentation conforme,”Rend. Circ. Mat. Palermo,23, 185–220 (1907).

    Article  MATH  Google Scholar 

  6. N. Tanaka, “On the pseudo-conformal geometry of hypersurfaces of the space ofn complex variables,”J. Math. Soc. Japan,14, 397–429 (1962).

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Pelles, “Proper holomorphic self-maps of the unit ball,”Math. Ann.,190, 298–305 (1971).

    Article  MathSciNet  Google Scholar 

  8. H. Alexander, “Holomorphic mappings from the ball and polydisc,”Math. Ann.,209, 249–256 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Tumanov and G. Khenkin, “Local characterization of holomorphic automorphisms of Siegel domains,”Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.],17, 49–61 (1983).

    MathSciNet  Google Scholar 

  10. A. Tumanov, “Finite dimensionality of the groupCR of automorphisms of standardCR manifolds and proper holomorphic mappings of Siegel domains,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],52, 651–659 (1988).

    MATH  Google Scholar 

  11. F. Forstnerič, “Mappings of quadric Cauchy-Riemann manifolds,”Math. Ann.,292, 163–180 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  12. S. Webster, “On the mapping problem for algebraic real hypersurfaces,”Invent. Math.,43, 53–68 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  13. A. B. Sukhov, “On algebraicity of complex-analytical sets,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],74, 419–426 (1993).

    MathSciNet  Google Scholar 

  14. R. A. Sharipov and A. B. Sukhov, “OnCR mappings between algebraic Cauchy-Riemann manifolds and separate algebraicity for homolorphic functions,” in:Preprint No. 95-3, Centre de Mathématiques et d’Informatique, Univ. de Provence, Laboratotoire d’Analyse, Topologie, Probabilités (Unité de Recherche Associée au CNRS 0225) (1995); “e-print alg-geom@publications.math.duke.edu/9412015.”

  15. R. A. Sharipov and A. B. Sukhov, “OnCR mappings between algebraic Cauchy-Riemann manifolds and separate algebraicity for holomorphic functions,”Trans. Amer. Math. Soc.,348, No. 2, 767–780 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  16. M. Reed and B. Simon,Methods of Modern Mathematical Physics, Academic Press, New York (1975).

    MATH  Google Scholar 

  17. A. N. Kolmogorov and S. V. Fomin,Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1972).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bashkortostan State University, USSR

    E. N. Tsyganov & R. A. Sharipov

Authors
  1. E. N. Tsyganov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. A. Sharipov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 294–302, August, 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tsyganov, E.N., Sharipov, R.A. Separate algebraicity along families of algebraic curves. Math Notes 68, 255–262 (2000). https://doi.org/10.1007/BF02675351

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02675351

Key words

Search

Navigation