Unirational variety

An algebraic variety over a field into which there exists a rational mapping from a projective space, , such that is dense in and the extension of the field of rational functions is separable. In other words, has a separable extension which is purely transcendental (cf. Transcendental extension).

Unirational varieties are close to rational varieties (cf. Rational variety), e.g. on a unirational variety there are no regular differential forms, for . The problem of the coincidence of rational and unirational varieties is called the Lüroth problem; the answer is negative.

References

[1]	I.R. Shafarevich, "Basic algebraic geometry" , Springer (1977) (Translated from Russian) MR0447223 Zbl 0362.14001