Skip to main content
Log in

Convexity properties of coverings of smooth projective varieties

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. Andreotti, A., Vesentini, E.: Carleman estimates for the Laplace-Beltrami equation on complex manifolds. Inst. Hautes Etudes Sci. Publ. Math25, 81–130 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bishop, E.: Mappings of partially analytic spaces. Am. J. Math.83, 209–242 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cartan, H.: Quotients of complex analytic spaces. In: Contributions to function theory, Internat. colloq. function theory, 1960. Bombay: Tata Institute of Fundamental Research 1960

    Google Scholar 

  4. Cheng, S.-Y., Yau, S.-T.: On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of Fefferman's equation. Comm. Pure Appl. Math.33, 507–544 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  5. Docquier, F., Grauert, H.: Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten. Math. Ann.140, 94–123 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  6. Grauert, H.: Bemerkenswerte pseudokonvexe Mannigfaltigkeiten. Math. Z.81, 377–391 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  7. Grauert, H.: Charakterisierung der holomorph vollständigen komplexen Räume. Math. Ann.129, 233–259 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  8. Grauert, H.: On Levi's problem and the imbedding of real analytic manifolds. Ann. Math.68, 460–472 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hartshorne, R.: Algebraic geometry. Graduate Texts in Math. 52. Berlin Heidelberg New York: Springer 1977

    Book  MATH  Google Scholar 

  10. Hörmander, L.: An introduction to complex analysis in several variables. Amsterdam New York: Elsevier 1973

    MATH  Google Scholar 

  11. Narasimhan, R.: Imbedding of holomorphically complete complex spaces. Am. J. Mat.82, 917–934 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  12. Narasimhan, R.: Imbedding of open Riemann surfaces. Nachr. Akad. Wiss. Gött.7, 159–165 (1960)

    MathSciNet  MATH  Google Scholar 

  13. Narasimhan, R.: The Levi problem for complex spaces. Math. Ann.142, 355–365 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  14. Narasimhan, R.: The Levi problem for complex spaces. II. Math. Ann.146, 195–216 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  15. Nori, M.V.: Zariski's conjecture and related problems. Ann. Sci. Ec. Norm. Super., IV. Ser.16, 305–344 (1983)

    MathSciNet  MATH  Google Scholar 

  16. Pinney, K.: Convexity results for domains in smooth projective varieties. Ph. D. thesis, Univ. of Chicago 1989

  17. Remmert, R.: Reduction of complex spaces. In: Seminars on analytic functions. Princeton: Inst. for Advanced Study 1957

    Google Scholar 

  18. Remmert, R.: Sur les espaces analytiques holomorphiquement séparables et holomorphiquement convexes. C. R. Acad. Sci. Paris,243, 118–121 (1956)

    MathSciNet  MATH  Google Scholar 

  19. Richberg, R.: Stetige streng pseudokonvexe Funktionen. Math. Ann.175, 257–286 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  20. Shafarevich, I.R.: Basic algebraic geometry. Translated by K. A. Hirsch. Berlin Heidelberg New York: Springer 1977

    MATH  Google Scholar 

  21. Siu, Y.-T.: Every Stein subvariety admits a Stein neighborhood. Invent. Math.38, 89–100 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  22. Stein, K.: Überlagerungen holomorph-vollständiger komplexer Räume. Arch. Math.7, 354–361 (1956)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

For H. Grauert on his sixtieth birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Napier, T. Convexity properties of coverings of smooth projective varieties. Math. Ann. 286, 433–479 (1990). https://doi.org/10.1007/BF01453583

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01453583

Keywords

Navigation