Algebraic Curves

  • I. R. Shafarevich
Part of the Encyclopaedia of Mathematical Sciences book series (volume 23)


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. [1985], Griffiths-Harris [1978], Hartshorne [1977], and Walker [1950].


Riemann Surface Complete Intersection Algebraic Variety Algebraic Curf Hyperelliptic Curve 
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© Springer-Verlag Berlin Heidelberg 1994

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  • I. R. Shafarevich

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