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.

Revised on November 2, 2012 21:32:30
by Zoran Škoda
(31.45.202.129)