In mathematics, a rational normal scroll is a ruled surface of degree n in projective space of dimension n + 1.
A non-degenerate irreducible surface of degree m – 1 in Pm is either a rational normal scroll or the Veronese surface.
Then the rational normal surface consists of all lines joining the points x and φ(x).
In the degenerate case when one of m or n is 0, the rational normal scroll becomes a cone over a rational normal curve.
If m < n then the rational normal curve of degree m is uniquely determined by the rational normal scroll and is called the directrix of the scroll.