Skip to main content

Concavity, convexity and complements in complex spaces

Part of the Lecture Notes in Mathematics book series (2766,volume 1194)

Keywords

  • Vector Bundle
  • Line Bundle
  • Complex Space
  • Normal Bundle
  • Holomorphic Vector Bundle

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adreotti, A. and H. Grauert: Théorèmes de finitude pour la cohomologie des espaces complexes. Bull. Soc. Math. France 90, 193–259 (1962).

    MathSciNet  MATH  Google Scholar 

  2. Barth, W.: Der Abstand von einer algebraischen Mannigfaltigkeit im komplex-projektiven Raum. Math. Ann. 187, 150–162 (1970).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Barth, W.: Transplanting cohomology classes in complex-projective space. Amer. Journ. of Math. 92, 951–967 (1970).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Fischer, G.: Complex analytic geometry. LNM 538. Springer Verlag, Berlin-Heidelberg-New York (1976).

    CrossRef  Google Scholar 

  5. Fritzsche, K.: q-konvexe Restmengen in kompakten komplexen Mannigfaltigkeiten. Math. Ann. 221, 251–273 (1976).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Fritzsche, K.: Pseudoconvexity properties of complements of analytic subvarieties. Math. Ann. 230, 107–122 (1977).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Fulton, W. and R. Lazarsfeld: Connectivity and its applications in algebraic geometry. LNM 862, Springer-Verlag, Berlin-Heidelberg-New York (1981).

    MATH  Google Scholar 

  8. Goldstein, N.: Ampleness andconnectedness in complex G/P. Trans. Amer. Math. Soc. 274, 361–373 (1982).

    MathSciNet  MATH  Google Scholar 

  9. Grauert, H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann. 146, 331–368 (1962).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Grauert, H. and O. Riemenschneider: Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen. Invent. Math. 11, 263–292 (1970).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Griffiths, P.: Hermitean differential geometry, Chern classes and positive vector bundles. In: Global Analysis. Papers in honor of K. Kodaira. (New York. Princeton Univ. Press (1969).

    Google Scholar 

  12. Hartshorne, R.: Ample vector bundles. Inst. Hautes Etudes Sci. Publ. Math. 29, 63–94 (1966).

    MathSciNet  MATH  Google Scholar 

  13. Hartshorne, R.: Cohomology of non-complete algebraic varieties. Compos. Math. 23, 257–264 (1971).

    MathSciNet  MATH  Google Scholar 

  14. Hartshorne, R.: Ample subvarieties of algebraic varieties. LNM 156, Springer Verlag, Berlin-Heidelberg-New York (1970).

    CrossRef  Google Scholar 

  15. Hironaka, H.: Bimeromorphic smoothing of complex analytic space. Math. Inst. Warwick Univ. England (1971).

    MATH  Google Scholar 

  16. Kobayashi, S.: Negative vector bundles and complex Finsler structures. Nagoya Math. Journ. 57, 153–166 (1975).

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Riemenschneider, O.: Characterizing Moisezon spaces by almost positive coherent sheaves. Math. Z. 123, 263–284 (1971).

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Schneider, M.: Über eine Vermutung von Hartshorne. Math. Ann. 201, 221–229 (1973).

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Schneider, M.: Tubenumgebungen Steinscher Räume. Manuscripta math. 18, 391–397 (1976).

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Sommese, A.: Submanifolds of Abelian varieties. Math. Ann. 233, 229–256 (1978).

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Sommese, A.: Concavity theorems. Math. Ann. 235, 37–53 (1978).

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. Sommese, A.: Complex subspaces of homogeneous complex manifolds. I. Transplanting theorems. Duke Journ. of Math. 46, 527–548 (1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. Sommese, A.: Complex subspaces of homogeneous complex manifolds. II. Homotopy results. Nagoya Math. Journ. 86, 101–129 (1982).

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. Sommese, A.: A convexity theorem. Proc. of Symp. in Pure Math. on Singularities, Arcata 1981, Vol. 40, part 2 497–505 (1983).

    MathSciNet  Google Scholar 

  25. Sommese, A. and A. Van de Ven: Homotopy groups of pullbacks of varieties. Preprint (1984).

    Google Scholar 

  26. Spallek, K.: Differenzierbare Räume. Math. Ann. 180, 269–296 (1969).

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Okonek, C. (1986). Concavity, convexity and complements in complex spaces. In: Grauert, H. (eds) Complex Analysis and Algebraic Geometry. Lecture Notes in Mathematics, vol 1194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076998

Download citation

  • DOI: https://doi.org/10.1007/BFb0076998

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16490-6

  • Online ISBN: 978-3-540-39829-5

  • eBook Packages: Springer Book Archive