Quartic Plane Curve

A quartic plane curve is a plane curve of the fourth degree. It can be defined by a quartic equation:

This equation has fifteen constants. However, it can be multiplied by any non-zero constant without changing the curve. Therefore, the space of quartic curves can be identified with the real projective space . It also follows that there is exactly one quartic curve that passes through a set of fourteen distinct points in general position, since a quartic has 14 degrees of freedom.

A quartic curve can have a maximum of:

  • Four connected components
  • Twenty-eight bi-tangents
  • Three ordinary double points.

Read more about Quartic Plane Curve:  Examples

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