Cremona Transformation

An entire Cremona transformation is a Birational Transformation of the Plane. Cremona transformations are Maps of the form

$$x_{i+1} = f(x_i,y_i)$$

$$y_{i+1} = g(x_i,y_i),$$

in which $f$ and $g$ are Polynomials. A quadratic Cremona transformation is always factorable.

See also Noether's Transformation Theorem

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 203-204, 1959.