A stably rational variety over a field 
is an integral algebraic
variety 
for which the Cartesian product 
is a rational variety
for some nonnegative integer 
. Thus stable rationality allows additional independent projective
coordinates before asking for a birational
transformation to projective space. In the
case of a smooth variety that is also a projective
variety over an algebraically closed field, a stably rational variety is a retract
rational variety and admits a decomposition
of the diagonal (Hotchkiss 2026).
Stably Rational Variety
See also
Algebraic Variety, Decomposition of the Diagonal, Projective Space, Rational Variety, Retract Rational VarietyExplore with Wolfram|Alpha
References
Hotchkiss, J. "The Rationality Problem for Hypersurfaces of Degree at Least Five." 7 Oct 2026. https://arxiv.org/abs/2610.10509.Cite this as:
Weisstein, Eric W. "Stably Rational Variety." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StablyRationalVariety.html