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Cremona Transformation

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

$\displaystyle x_{i+1}$ $\textstyle =$ $\displaystyle f(x_i,y_i)$  
$\displaystyle y_{i+1}$ $\textstyle =$ $\displaystyle g(x_i,y_i),$  

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

See also Noether's Transformation Theorem


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

© 1996-9 Eric W. Weisstein