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Introduction to Algebraic Geometry

  • Ian F. Blake
  • XuHong Gao
  • Ronald C. Mullin
  • Scott A. Vanstone
  • Tomik Yaghoobian
Chapter
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 199)

Abstract

In this chapter some of the basic concepts of algebraic geometry needed for algebraic geometric codes will be presented. Since the theory of algebraic geometry is both vast and deep, we can only give a rough outline here. Emphasis will be placed on making the ideas intuitive and clear enough to enable the reader to understAnd the algebraic geometric codes. The majority of this chapter is based on the treatment of Fulton [2]. For a more complete treatment of algebraic geometry the reader should consult that reference, or the recent book by Moreno [4]. Some other stAndard textbooks in algebraic geometry are [1, 3, 7, 9].

Keywords

Algebraic Geometry Prime Ideal Function Field Tangent Line Algebraic 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.

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References

  1. [1]
    C. Chevalley, Introduction to the Theory of Algebraic Functions of One Variable, A.M.S. Math. Surveys, New York, 1951.zbMATHGoogle Scholar
  2. [2]
    W. Fulton, Algebraic Curves, Benjamin, New York, 1969.zbMATHGoogle Scholar
  3. [3]
    R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977.zbMATHCrossRefGoogle Scholar
  4. [4]
    C. Moreno, Algebraic Curves over Finite Fields, Cambridge University Press, 1991.zbMATHCrossRefGoogle Scholar
  5. [5]
    J.-P. Serre, “Sur le nombre de points rationnels d’une corbe algébrique sur un corps fini”, C.R. Acad. Sci. Paris Sér. 1, 296 (1983), 397–402.zbMATHGoogle Scholar
  6. [6]
    J.-P. Serre, “Nombres de points des courbes algébriques sur F q” Séminaire de Théorie des Nombres, Bordeaux, 22 (1983), 1–8.Google Scholar
  7. [7]
    I. Shafarevich, Basic Algebraic Geometry, Springer-Verlag, New York, 1977.zbMATHGoogle Scholar
  8. [8]
    J.H. Van Lint and G. Van Der Geer, Introduction to Coding Theory and Algebraic Geometry, Dmv Seminar, BAnd 12, Birkhauser Verlag, 1988.zbMATHCrossRefGoogle Scholar
  9. [9]
    R.J. Walker, Algebraic Curves, Dover, New York, 1962.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Ian F. Blake
    • 1
  • XuHong Gao
    • 1
  • Ronald C. Mullin
    • 1
  • Scott A. Vanstone
    • 1
  • Tomik Yaghoobian
    • 1
  1. 1.University of WaterlooCanada

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