Skip to main content
SpringerLink
Log in

Zariski Decomposition and Applications

  • Chapter
Algebraic Surfaces

Part of the book series: Universitext ((UTX))

  • 2119 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 89.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographic References

  1. L. Bâdescu, Anticanonical models of ruled surfaces. Ann. Univ.Ferrara 29 (1983), 165–177.

    MATH  Google Scholar 

  2. 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. L. Brenton, Some algebraicity criteria for singular surfaces.Invent. Math.41 (1977), 129–147.

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Fujita, On Zariski problem.Proc. Japan. Acad.55 (1979), 106–110.

    Article  MATH  Google Scholar 

  5. 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. F. Sakai, Enriques’ classification of normal Gorenstein surfaces.Amer. J. Math.104 (1981), 1233–1241.

    Article  Google Scholar 

  7. F. Sakai, Anticanonical models of rational surfaces.Math. Ann.269 (1984), 389–410.

    Article  MathSciNet  MATH  Google Scholar 

  8. O. Zariski, The theorem of Riemann—Roch for high multiples of a divisor on an algebraic surface.Ann. of Math.76 (1962), 560–612.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Romanian Academy, PO Box 1-764, 70700, Bucharest, Romania

    Lucian Bădescu

Authors
  1. Lucian Bădescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media New York

About this chapter

Cite this chapter

Bădescu, L. (2001). Zariski Decomposition and Applications. In: Algebraic Surfaces. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3512-3_14

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3512-3_14

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-3149-8

  • Online ISBN: 978-1-4757-3512-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation