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Mathematical Notes

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

Strictly pseudoconvex domains and algebraic varieties

  • S. Yu. Nemirovskii
Article
  • 59 Downloads

Abstract

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 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

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

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