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 in the intersection
of their domains. For irreducible
varieties, a rational map is dominant when the image
of any representative is dense in 
.
A birational transformation is a dominant
rational map with a rational inverse (Stacks Project Authors 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