A rational map 
between algebraic varieties is an equivalence
class of morphisms 
defined on dense open
subsets 
.
Two representatives define the same rational map iff they
agree on a dense open set of
the intersection of their domains. A rational map is dominant when its image is dense in 
. A birational transformation
is a dominant rational map with a rational inverse (Stacks Project 2026).
Rational Map
See also
Algebraic Variety, Birational Transformation, Morphism, Rational Function, Rational VarietyExplore with Wolfram|Alpha
References
The Stacks Project Authors. "Rational Maps." §29.50 in The Stacks Project, Tag 01RR, 2026. https://stacks.math.columbia.edu/tag/01RR.Cite this as:
Weisstein, Eric W. "Rational Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RationalMap.html