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.
KeywordsElliptic Curve Complete Intersection Elliptic Curf Hyperelliptic Curve Quadric Surface
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