A birational transformation of algebraic varieties is a dominant rational map with a rational inverse. Equivalently, it restricts to an isomorphism between dense open subsets.
Birational Transformation
See also
Algebraic Variety, Birational Morphism, Minimal Model Program, Rational Map, Rational Variety, Riemann Curve Theorem, Weber's TheoremExplore 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.Referenced on Wolfram|Alpha
Birational TransformationCite this as:
Weisstein, Eric W. "Birational Transformation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BirationalTransformation.html