Zariski Decomposition and Applications

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


In this chapter we present Zariski’s theory of finite generation of the graded algebra R (X, D) associated to a divisor D on a surface X, cf. [Zar1] and some more recent developments related to this theory.


Cartier Divisor Ample Divisor Canonical Divisor Algebraic Space Exceptional Curve 
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. [Bâd2*]
    L. Bâdescu, Anticanonical models of ruled surfaces. Ann. Univ.Ferrara 29 (1983), 165–177.zbMATHGoogle Scholar
  2. [Bâd3*]
    L. Bâdescu, The graded algebra associated to a divisor on a smooth projective surface (in Romanian). InAnalizé Complexé: Aspecte Clasice si Moderne. Editura Stiintificâ §i Enciclopedicâ, Bucuresti, 1988. 295–337.Google Scholar
  3. [Bre*]
    L. Brenton, Some algebraicity criteria for singular surfaces.Invent. Math.41 (1977), 129–147.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [Fuj*]
    T. Fujita, On Zariski problem.Proc. Japan. Acad.55 (1979), 106–110.zbMATHCrossRefGoogle Scholar
  5. [Mum6*]
    D. Mumford, Hilbert’s fourteenth problem—the finite generation of subrings such as rings of invariants. InMathematical Developments Arising from Hilbert’s Problems, Proc. Symposia in Pure Math. 28, Part 2, Amer. Math. Soc., Providence, Rhode Island, 1976, 431–444.Google Scholar
  6. [Sak1*]
    F. Sakai, Enriques’ classification of normal Gorenstein surfaces.Amer. J. Math.104 (1981), 1233–1241.CrossRefGoogle Scholar
  7. [Sak3*]
    F. Sakai, Anticanonical models of rational surfaces.Math. Ann.269 (1984), 389–410.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [Zar1]
    O. Zariski, The theorem of Riemann—Roch for high multiples of a divisor on an algebraic surface.Ann. of Math.76 (1962), 560–612.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

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

Personalised recommendations