Ruled Variety

(Algebraic Geometry)

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Algebraic Geometry
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What is 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.

Technology Types

algebraic geometry

Synonyms

Uniruled variety

Translations

선직다양체 (ko)単線織多様体 (ja)

Tech Info


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