• Robin Hartshorne
Part of the Graduate Texts in Mathematics book series (GTM, volume 52)


In this chapter we apply the techniques we have learned earlier to study curves. But in fact, except for the proof of the Riemann-Roch theorem (1.3), which uses Serre duality, we use very little of the fancy methods of schemes and cohomology. So if a reader is willing to accept the statement of the Riemann-Roch theorem, he can read this chapter at a much earlier stage of his study of algebraic geometry. That may not be a bad idea, pedagogically, because in that way he will see some applications of the general theory, and in particular will gain some respect for the significance of the Riemann-Roch theorem. In contrast, the proof of the Riemann-Roch theorem is not very enlightening.


Elliptic Curve Complete Intersection Elliptic Curf Hyperelliptic Curve Quadric Surface 
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Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • Robin Hartshorne
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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