In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means that its function field is isomorphic to

${\displaystyle K(U_{1},\dots ,U_{d}),}$

the field of all rational functions for some set ${\displaystyle \{U_{1},\dots ,U_{d}\}}$ of indeterminates, where d is the dimension of the variety.