nLab birational map

A rational map $f: X \dashrightarrow Y$ of varieties is birational if there is a rational map $g: Y \dashrightarrow X$ such that both compositions $g\circ f$ and $f\circ g$ are defined as rational maps and equal the identity. Two varieties are birational (synonyms: birationally isomorphic, birationally equivalent) if there is a birational map between them. See birational geometry.

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