Rational map

Summary

A rational map from a variety $X$ to a variety $Y$ is a morphism defined on some nonempty open subset of $X$. Two such morphisms give the same rational map when they agree on a common open subset. It is written $X \dashrightarrow Y$, because it may fail to be defined at some points. Rational maps are the maps of birational geometry, which studies varieties up to changes on lower-dimensional subsets.