Algebraic geometry Birational geometry Concept
Rational variety
Summary
A rational variety is a variety that is birationally equivalent to projective space. Its points can be parametrised, on a dense open set, by rational functions of independent parameters. Deciding which varieties are rational is one of the oldest problems of birational geometry. Every rational variety is unirational, and the converse fails in dimension over .
Further reading
About this page
| Tag | XV4K9GREJ9 |
|---|---|
| URI | m2://XV4K9GREJ9 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 14M20, 14E08 |
| Specializes | Unirational variety |
| Same as | |
| Changed | 2 November 2026 |
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