Skip to main content

On the affine-ruledness of algebraic varieties

Curves, Surfaces, Threefolds, …

Part of the Lecture Notes in Mathematics book series (LNM,volume 1016)

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   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
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. Fujita, T.: On Zariski problem. Proc. Japan Acad. 55, Ser.A. (1979), 106–110.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Iitaka,S.: On logarithmic Kodaira dimension of algebraic varieties. Complex analysis and algebraic geometry. A collection of papers dedicated to K. Kodaira, 175–189. Iwanami Shoten Publishers-Cambridge Univ. Press, 1977.

    Google Scholar 

  3. Kambayashi, T.: On Fujita’s strong cancellation theorem for the affine plane. J. Fac. Sci. Univ. Tokyo 27 (1980), 535–548.

    MathSciNet  MATH  Google Scholar 

  4. Maruyama, M.: On classification of ruled surfaces. Lectures in Mathematics 3. Kyoto University. Tokyo: Kinokuniya 1970.

    MATH  Google Scholar 

  5. Miyanishi, M.: An algebraic characterization of the affine plane. J. Math. Kyoto Univ. 15 (1975), 169–184.

    MathSciNet  MATH  Google Scholar 

  6. Miyanishi, M., Sugie, T.: Affine surfaces containing cylinderlike open sets. J. Math. Kyoto Univ. 20 (1980), 11–42.

    MathSciNet  MATH  Google Scholar 

  7. Miyanishi, M.: Non-complete algebraic surfaces. Lecture Notes in Mathematics 857. Berlin-Heidelberg-New York: Springer 1981.

    MATH  Google Scholar 

  8. Miyanishi,M.: On affine-ruled irrational surfaces. To appear in Invent. Math.

    Google Scholar 

  9. Miyanishi,M.: An algebro-topological characterization of the affine space of dimension three. Forthcoming.

    Google Scholar 

  10. Mori, S.: Threefolds whose canonical bundles are not numerically effective. Ann. of Math. 116 (1982), 133–176.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Russell, P.: On affine-ruled surfaces. Math. Ann. 255 (1981), 287–302.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Sugie, T.: Characterization of surfaces containing cylinderlike open sets. Osaka J. Math. 17 (1980), 363–376.

    MathSciNet  MATH  Google Scholar 

  13. Swan, R.: Notes at the University of Chicago, 1979.

    Google Scholar 

  14. Tsunoda, S., Miyanishi, M.: The structure of open algebraic surfaces, II. To appear in the proceedings of the Taniguchi Symposium on Algebraic Geometry (Katata), 1982.

    Google Scholar 

  15. Brieskorn, E.: Rationale Singularitäten komplexer Flächen. Invent. Math. 4 (1968), 336–358.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Miyanishi, M.: Lectures on curves on rational and unirational surfaces. Tata Institute of Fundamental Research. Bombay, 1978. Berlin-Heidelberg-New York: Springer, 1978.

    Google Scholar 

  17. Tsunoda, S., Miyanishi, M.: On the structure of non-complete algebraic surfaces with logarithmic Kodaira dimension-∞ and with non-connected boundaries at infinity. Forthcoming.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Miyanishi, M. (1983). On the affine-ruledness of algebraic varieties. In: Raynaud, M., Shioda, T. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 1016. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099975

Download citation

  • DOI: https://doi.org/10.1007/BFb0099975

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12685-0

  • Online ISBN: 978-3-540-38676-6

  • eBook Packages: Springer Book Archive