In mathematics, the rational normal curve is a smooth, rational curve C of degree n in projective n-space Pn. It is a simple example of a projective variety;...

= 1 , {\displaystyle n=1,} the Veronese variety is known as the rational normal curve, of which the lower-degree examples are familiar. For n = 1 , d...

complete intersection. It is the three-dimensional case of the rational normal curve, and is the image of a Veronese map of degree three on the projective...

lemniscate Quartic plane curve Rational normal curve Riemann–Roch theorem for algebraic curves Weber's theorem (Algebraic curves) Riemann–Hurwitz formula...

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...

relevant variables are normally distributed. A normal distribution is sometimes informally called a bell curve. However, many other distributions are bell-shaped...

When C is a hyperelliptic curve, the canonical curve is a rational normal curve, and C a double cover of its canonical curve. For example if P is a polynomial...

moment curve is a parabola, and in three-dimensional space it is a twisted cubic. Its closure in projective space is the rational normal curve. Moment...

This is the meaning of "normal" in the phrases rational normal curve and rational normal scroll. Every regular scheme is normal. Conversely, Zariski (1939...

convex polytope formed as a convex hull of n distinct points on a rational normal curve in Rd, where n is greater than d. These polytopes were studied by...

Poinsot's spirals Rational normal curve Rose curve Bicuspid curve Cassini oval Cassinoide Cubic curve Elliptic curve Watt's curve Butterfly curve Elkies trinomial...

mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over...

Hypotrochoid Lissajous curve Poinsot's spirals Rational normal curve Rose curve Bicuspid curve Cassinoide Cubic curve Elliptic curve Watt's curve Bolza surface...

(straight) lines. It can also be defined as a curve whose points are at a constant normal distance from a given curve. These two definitions are not entirely...

variety X. See also function field (scheme theory). rational normal curve A rational normal curve is the image of P 1 → P d , ( s : t ) ↦ ( s d : s d...

of projective spaces Rational normal curve Conics, Pascal's theorem, Brianchon's theorem Twisted cubic Elliptic curve, cubic curve Elliptic function, Jacobi's...

A rational curve is a curve that is birationally equivalent to a projective line (see rational variety); its genus is 0. A rational normal curve in projective...

even in the case of curves. There are examples where the minimal free resolution is known explicitly. For a rational normal curve it is an Eagon–Northcott...

P1 are depicted by a rational normal curve in Pn, then the group of the projective transformations of Pn that preserve the curve is isomorphic to the...

algebraic curve is an algebraic curve that is complete as an algebraic variety. A projective curve, a dimension-one projective variety, is a complete curve. A...

give ample examples of rational maps which are not birational. For example, Belyi's theorem states that every algebraic curve C {\displaystyle C} admits...

closed immersion for d ≥ 1 {\displaystyle d\geq 1} , with image a rational normal curve of degree d in P d {\displaystyle \mathbb {P} ^{d}} . Therefore...

parallel. In algebraic geometry, the parabola is generalized by the rational normal curves, which have coordinates (x, x2, x3, ..., xn); the standard parabola...

choice theory, the income-consumption curve (also called income expansion path and income offer curve) is a curve in a graph in which the quantities of...

Instead, it is a two-to-one cover of the canonical curve of C, which is a rational normal curve. The Iitaka dimension of the canonical bundle of a smooth...

gave us the notion of so-called rational expectations.) Expectational equilibrium gives us the long-term Phillips curve. First, with λ less than unity:...

space curve for all t in the instantaneous direction of motion. At t = c, the space curve has a tangent vector dr(t)/dt|t = c, and the hyperplane normal to...

(conic section) Directrix (ellipse) Directrix (generatrix) Directrix (rational normal scroll) Directrix is a spaceship in the Lensman series of novels by...

In algebraic geometry, the normal degree of a rational curve C on a surface is defined to be –K.C–2 where K is the canonical divisor of the surface. Sommese...

Castelnuovo described the curves satisfying this bound, showing in particular that they lie on either a rational normal scroll or on the Veronese surface...