nLab
birational map

A rational map f:XYf: X \dashrightarrow Y of varieties is birational if there is a rational map g:YXg: Y \dashrightarrow X such that both compositions gfg\circ f and fgf\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)