Its closure in projective space is the rational normal curve.

This is a broad family of rational cubic curves containing several well-known examples.

Normal degree of a rational curve on a surface.

For a rational normal curve it is an Eagon-Northcott complex.

An example would be the rational normal curve.

This representation as the "weighted control points" and weights is often convenient when evaluating rational curves.

The rational normal curve has an assortment of nice properties:

This property distinguishes the rational normal curve from all other curves.

This was verified for degrees up to 7 by who also calculated the number 609250 of degree 2 rational curves.

For the Veronese variety is known as the rational normal curve, of which the lower-degree examples are familiar.