Algebraic geometry

Ruled variety

In algebraic geometry, a variety over a field k is ruled if it is birational to the product of the projective line with some variety over k. A variety is uniruled if it is covered by a family of rational curves. (More precisely, a variety X is uniruled if there is a variety Y and a dominant rational map Y × P1 – → X which does not factor through the projection to Y.) The concept arose from the ruled surfaces of 19th-century geometry, meaning surfaces in affine space or projective space which are covered by lines. Uniruled varieties can be considered to be relatively simple among all varieties, although there are many of them. (Wikipedia).

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Related pages

Birational geometry | Abelian variety | Smooth scheme | Algebraically closed field | Kummer variety | Finite field | Rational mapping | Algebraic variety | Projective space | Projective variety | Hypersurface | Separable extension | Kodaira dimension | Rational variety | Characteristic (algebra) | Jean-Pierre Demailly | Field (mathematics) | Canonical bundle | Real number | Algebraic geometry | Ruled surface | Glossary of algebraic geometry | Divisor (algebraic geometry) | Affine space | Complex number | Adjunction formula | Fano variety | Supersingular elliptic curve