Advertisement

Plücker, Hesse, Higher Plane Curves, and the Resolution of the Duality Paradox

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

An algebraic plane curve is, by definition, the locus in the plane corresponding to a polynomial equation of some degree, n: f (x,y) = 0. For example x 3 y + y3 + x = 0 represents a quartic. The equation may be written in homogeneous coordinates [x,y,z] by setting x = x′/z′, y = y′/z′ and multiplying through by the lowest power of z′ that produces a polynomial equation (if you wish you may then remove the primes) when the curve is considered to lie in the projective plane. The example above becomes x3y + y3z + z3x = 0 in homogeneous form.

Keywords

Double Point Analytic Geometry External Point Quartic Curve Dual Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag London Limited 2007

Personalised recommendations