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Y by definition gives a birational map f : X ⇢ Y. In this case, X and Y are said to be birational, or birationally equivalent. In algebraic terms, two...

list of algebraic surfaces. The first five examples are in fact birationally equivalent. That is, for example, a cubic surface has a function field isomorphic...

contracted. Then, the birational map is given by normalization. Two varieties are said to be birationally equivalent if there exists a birational map between them;...

is generated by the base point.[citation needed] The curve is birationally equivalent to a twisted Edwards curve used in the Ed25519 signature scheme...

Equivalently, they are birationally equivalent if their function fields are isomorphic. An affine variety is a rational variety if it is birationally...

(up to birational equivalence) and algebraic function fields in one variable over F holds in general. Two curves can be birationally equivalent (i.e. have...

Labyrinth, a unicursal maze Unicursal curve, a curve which is birationally equivalent to a line Unicursal hexagram, a star polygon This disambiguation...

b=256} . The curve E ( F q ) {\displaystyle E(\mathbb {F} _{q})} is birationally equivalent to the Montgomery curve known as Curve25519. The equivalence is...

variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means that...

(non-singular) curve of genus 0 is rationally equivalent over K to a conic C, which is itself birationally equivalent to projective line if and only if C has...

the birational equivalence between Montgomery curves and twisted Edwards curve: Theorem (i) Every twisted Edwards curve is birationally equivalent to a...

} where c, d ∈ K with cd(1 − c4·d) ≠ 0. Every Edwards curve is birationally equivalent to an elliptic curve in Montgomery form, and thus admits an algebraic...

comes from an algebraic curve, well defined up to birational equivalence and two birational equivalent curves give the same surface. Therefore, the Riemann...

5-sphere, i.e. torsion. In birational geometry, a complex rational surface is any algebraic surface birationally equivalent to the complex projective plane...

reduces to an ordinary Edwards curve. Every twisted Edwards curve is birationally equivalent to an elliptic curve in Montgomery form and vice versa. As for...

algebraic function field of n variables over k. Two varieties are birationally equivalent if and only if their function fields are isomorphic. (But note...

geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety of...

{\displaystyle y={\frac {Y}{Z}}} and a, d in K Note that these curves are birationally equivalent to Hessian curves. The Hessian curve is just a special case of...

A2(2) is birationally equivalent to the Segre cubic which is in fact rational. Similarly, a compactification of A2(3) is birationally equivalent to the...

dimension 3 flips are used to construct minimal models, and any two birationally equivalent minimal models are connected by a sequence of flops. It is conjectured...