Plane Curves and Algebra

Audun Holme ()
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Audun Holme: University of Bergen, Department of Mathematics

Chapter Chapter 4 in A Royal Road to Algebraic Geometry, 2012, pp 63-118 from Springer

Abstract: Abstract The affine and homogeneous coordinate rings are introduced, as well as multiplicity of points and intersection multiplicity. A complete treatment of intersection multiplicity for curves in the projective plane is given here. As will be noted in the exercises, this treatment goes over with minor adaptations to an intersection theory for curves on a smooth projective surface. Also treated in this chapter are a rudimentary start on linear systems of curves, Bézout’s theorem, simple elimination theory with application to the twisted cubic curve, points of inflexion and the Hessian.

Keywords: Intersection Multiplicity; Affine Coordinate Ring; Smooth Projective Surface; Limited Affinity; Homogeneous Prime Ideals (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-642-19225-8_4

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