Algebraic Curves

  • Joseph H. Silverman
Part of the Graduate Texts in Mathematics book series (GTM, volume 106)


In this chapter we present the basic facts about algebraic curves (i.e. projective varieties of dimension 1) which will be needed for our study of elliptic curves. (Actually, since elliptic curves are curves of genus 1, one of our tasks will be to define the genus of a curve.) As in Chapter I, we give references for those proofs which are not included. There are many books where the reader can find more material on the subject of algebraic curves, for example [Har, Ch. IV], [Sha 2], [G–H, Ch. 2], [Wa].


Smooth Curve Elliptic Curf Function Field Algebraic Curf Smooth Curf 
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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Joseph H. Silverman
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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