Cohomological Intersection Theory and the Nakai—Moishezon Criterion of Ampleness

  • Lucian Bădescu
Part of the Universitext book series (UTX)


In this chapter we present, following Kleiman [Kle], the cohomological theory of intersection, the Nakai—Moishezon criterion of ampleness for divisors, and some of its more important consequences. Furthermore, we prove that every nonsingular complete surface is projective.


Exact Sequence Integral Curve Intersection Theory Cartier Divisor Closed Subscheme 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographic References

  1. [Kle]
    S. Kleiman, Towards a numerical theory of ampleness. Ann. Of Math. 84 (1966), 293–344.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [Har1]
    R. Hartshorne, Algebraic Geometry. Graduate Texts in Mathematics 52, Springer-Verlag, New York, 1977.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Lucian Bădescu
    • 1
  1. 1.Institute of MathematicsRomanian AcademyBucharestRomania

Personalised recommendations