Algebraic geometry Birational geometry Concept
Unirational variety
Summary
A unirational variety is a variety that is dominated by projective space through a rational map. Its points can be parametrised by rational functions, but the parametrisation may cover each point several times. Every rational variety is unirational. Whether the converse holds is the Lüroth problem. It holds for curves, and for surfaces over an algebraically closed field of characteristic , but it fails for some threefolds over .
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| Tag | YF1SE8WJK3 |
|---|---|
| URI | m2://YF1SE8WJK3 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 14M20, 14E08 |
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