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Difference between revisions of "Unirational variety"

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<table><TR><TD valign="top">[1]</TD> <TD valign="top"> I.R. Shafarevich,   "Basic algebraic geometry" , Springer (1977) (Translated from Russian)</TD></TR></table>
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<table><TR><TD valign="top">[1]</TD> <TD valign="top"> I.R. Shafarevich, "Basic algebraic geometry" , Springer (1977) (Translated from Russian) {{MR|0447223}} {{ZBL|0362.14001}} </TD></TR></table>

Revision as of 21:57, 30 March 2012

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
How to Cite This Entry:
Unirational variety. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unirational_variety&oldid=24003
This article was adapted from an original article by Vik.S. Kulikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article