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Algebraic Curves

In: An Algebraic Approach to Geometry

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  • Francis Borceux

    (Université catholique de Louvain)

Abstract

The complex projective plane is the natural efficient context where to study algebraic curves: curves whose equation is polynomial. We study the questions of tangency, singularity, multiplicity, inflexion points. We investigate the number of intersection points of two curves and prove various versions of the corresponding Bezout theorem. We pay special attention to the cubics, the properties of their inflexion points and the abelian group attached to them. We also investigate the rational curves: those admitting parametric equations in terms of rational fractions.

Suggested Citation

  • Francis Borceux, 2014. "Algebraic Curves," Springer Books, in: An Algebraic Approach to Geometry, edition 127, chapter 0, pages 267-340, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-01733-4_7
    DOI: 10.1007/978-3-319-01733-4_7
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