Editing Birational geometry (section)

=== Rational maps ===
A [[rational mapping|rational map]] from one variety (understood to be [[Irreducible component|irreducible]]) <math>X</math> to another variety <math>Y</math>, written as a dashed arrow {{nowrap|''X'' {{font|size=145%|⇢}}''Y''}}, is defined as a [[algebraic geometry#Morphism of affine varieties|morphism]] from a nonempty open subset <math>U \subset X</math> to <math>Y</math>. By definition of the [[Zariski topology]] used in algebraic geometry, a nonempty open subset <math>U</math> is always dense in <math>X</math>, in fact the complement of a lower-dimensional subset. Concretely, a rational map can be written in coordinates using rational functions.