The intersection of plane curves

Egbert Brieskorn and Horst Knörrer
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Egbert Brieskorn: Universität Bonn, Mathematisches Institut
Horst Knörrer: Universität Bonn, Mathematisches Institut

Chapter 6 in Plane Algebraic Curves, 1986, pp 227-278 from Springer

Abstract: Abstract In this section we shall prove the main result in the intersection theory of plane algebraic curves, Bézout’s theorem (1779). This theorem gives the precise number of intersection points of two plane curves C, C′ in the complex projective plane P2(ℂ). To be sure, the points of intersection must be chosen with suitable multiplicity, and defining this intersection multiplicity is a problem in itself. Here we shall choose a definition which makes the proof of Bézout’s theorem particularly simple.

Keywords: Singular Point; Intersection Point; Homogeneous Polynomial; Intersection Number; Homology Class (search for similar items in EconPapers)
Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-5097-1_6

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DOI: 10.1007/978-3-0348-5097-1_6

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