Mathematical Notes

, Volume 60, Issue 3, pp 306–312 | Cite as

Strictly pseudoconvex domains and algebraic varieties

  • S. Yu. Nemirovskii


In the paper, we consider applications of strictly pseudoconvex domains to the problems of algebraicity and rationality. We give a new proof of the Kodaira theorem on the algebraicity of a surface and we also prove a multidimensional version of this theorem. Theorems analogous to the Hodge index theorem and the Lefschetz theorem about (1, 1)-classes are obtained for strictly pseudoconvex domains. Conjectures on the geometry of strictly pseudoconvex domains on algebraic surfaces are formulated.

Key words

compact complex manifold algebraic variety strictly pseudoconvex domain Hodge index theorem rational algebraic surface 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Grauert, “Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen,” Inst. Hautes Études,5, (1960).Google Scholar
  2. 2.
    R. C. Gunning and H. Rossi,Analytic Functions of Several Complex Variables, Prentice-Hall Inc., Englewood Cliffs, N.J. (1965).Google Scholar
  3. 3.
    O. Suzuki, “Neighborhoods of a smooth compact algebraic curve embedded in a 2-dimensional complex manifold,”Publ. Res. Inst. Math. Sci. Ser. A.,11, No. 1, 185–199 (1975).MATHGoogle Scholar
  4. 4.
    I. R. Shavarevich,Foundations of Algebraic Geometry [in Russian], Vol. 1, 2, Nauka, Moscow (1986).Google Scholar
  5. 5.
    K. Kodaira, “On compact analytic surfaces. I,” in:Analytic Functions, Princeton Univ. Press, Princeton, N.J. (1960), pp. 121–135.Google Scholar
  6. 6.
    Ph. Griffits and J. Harris,Principles of Algebraic Geometry, Wiley-Interscience Publ., New York-Chichester-Brisbane-Toronto (1978).Google Scholar
  7. 7.
    W. Barth, C. Peters, and A. Van de Ven,Compact Complex Surfaces, Springer-Verlag, New York (1984).Google Scholar
  8. 8.
    R. Wells,Differential Analysis on Complex Manifolds, Prentice-Hall Inc. (1973).Google Scholar
  9. 9.
    H. Grauert and R. Remmert,Coherent Analytic Sheaves, Springer-Verlag, New York (1984).Google Scholar
  10. 10.
    S. Ivashkovich and V. Shevchishin,Pseudoholomorphic Curves and Envelopes of Meromorphy, Preprint, Bochum (1994).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • S. Yu. Nemirovskii
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

Personalised recommendations