be understood as a mapping to the dual space of polynomials on V. This is because for fields with finite characteristic p, the pth powers of elements of V are not rational normal curves, but are of course a line. (See, for example additive polynomial for a treatment of polynomials over a field of finite characteristic). Rational normal curve For the Veronese variety is known as the rational normal curve, of which the lower-degree examples are familiar. For the Veronese map is simply the identity map on the projective line. For the Veronese variety is the standard parabola in affine coordinates For the Veronese variety is the twisted cubic, in affine coordinates Biregular The image of a variety under the Veronese map is again a variety, rather than simply a constructible set; furthermore, these are isomorphic in the sense that the inverse map exists and is regular – the Veronese map is biregular. More precisely, the images of open sets in the Zariski topology are again open. See also The Veronese surface is the only Severi variety of dimension 2 References Joe Harris, Algebraic Geometry, A First Course, (1992) Springer-Verlag, New York. Algebraic varieties Algebraic surfaces Complex surfaces Tensors