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 
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Bibliographic References

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    L. Bâdescu, Anticanonical models of ruled surfaces. Ann. Univ.Ferrara 29 (1983), 165–177.MATHGoogle Scholar
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    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
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    O. Zariski, The theorem of Riemann—Roch for high multiples of a divisor on an algebraic surface.Ann. of Math.76 (1962), 560–612.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

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

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