Algebraic Curves

Francis Borceux
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Francis Borceux: Université catholique de Louvain

Chapter Chapter 7 in An Algebraic Approach to Geometry, 2014, pp 267-340 from Springer

Abstract: 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.

Keywords: Intersection Point; Inflexion Point; Double Point; Algebraic Curve; Algebraic Curf (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-01733-4_7

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DOI: 10.1007/978-3-319-01733-4_7

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