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Unirational variety

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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)
How to Cite This Entry:
Unirational variety. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unirational_variety&oldid=13973
This article was adapted from an original article by Vik.S. Kulikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article