In the present chapter an algebraic curve is regarded as an object of external geometry. The main results on projective embeddings — properties and constructions — are discussed in §3. Of major interest here are the highlights of the enumerative geometry of curves: Castelnuovo’s inequality and the formulae of Clebsch and Plücker. The required notions and techniques are introduced in the first two sections. A detailed treatment of the material of this chapter, and proofs, can be found in Arbarello et al. , Griffiths-Harris , Hartshorne , and Walker .
KeywordsRiemann Surface Complete Intersection Algebraic Variety Algebraic Curf Hyperelliptic Curve
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