A retract rational variety, in the smooth projective case over an algebraically closed field 
, is an algebraic variety 
admitting a dominant rational map 
with a rational map
serving as a section 
, so that 
is the identity map.
Every stably rational variety is retract
rational. A retract rational variety admits a decomposition
of the diagonal (Hotchkiss 2026).
Retract Rational Variety
See also
Algebraic Variety, Decomposition of the Diagonal, Projective Space, Rational Variety, Stably 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. "Retract Rational Variety." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RetractRationalVariety.html