| dbo:abstract |
En géométrie algébrique, une variété rationnelle est une variété algébrique (intègre) V sur un corps K qui est birationnelle à un espace projectif sur K, c'est-à-dire qu'un certain ouvert dense de V est isomorphe à un ouvert d'un espace projectif. De façon équivalente, cela signifie que son corps de fonctions est isomorphe au corps des fractions rationnelles à d indéterminées K(U1, … , Ud), l'entier d étant alors égal à la dimension de la variété. (fr) In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means that its function field is isomorphic to the field of all rational functions for some set of indeterminates, where d is the dimension of the variety. (en) 数学では、与えられた体 K 上で定義された代数多様体で K 上のある次元の射影空間と双有理同値な代数多様体を、有理多様体(rational variety)と言う。有理多様体は、代数多様体上の函数体が、ある不定元の集合 の有理函数の体 に同型であることを意味する。ここの d は、(dimension of an algebraic variety)である。 (ja) 대수기하학에서 유리 다양체(有理多樣體, 영어: rational variety)는 사영 공간과 쌍유리 동치인 대수다양체이다. (ko) 在數學中的代數幾何領域，域 上的有理簇是一個雙有理等價於射影空間 （）的代數簇。有理性僅依賴於其函數域，更明確地說，代數簇 是有理簇若且唯若 ，其中 是獨立的變元。 (zh) |
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Richard Swan (en) |
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R. G. (en) |
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Swan (en) |
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1969 (xsd:integer) |
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| rdfs:comment |
En géométrie algébrique, une variété rationnelle est une variété algébrique (intègre) V sur un corps K qui est birationnelle à un espace projectif sur K, c'est-à-dire qu'un certain ouvert dense de V est isomorphe à un ouvert d'un espace projectif. De façon équivalente, cela signifie que son corps de fonctions est isomorphe au corps des fractions rationnelles à d indéterminées K(U1, … , Ud), l'entier d étant alors égal à la dimension de la variété. (fr) In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means that its function field is isomorphic to the field of all rational functions for some set of indeterminates, where d is the dimension of the variety. (en) 数学では、与えられた体 K 上で定義された代数多様体で K 上のある次元の射影空間と双有理同値な代数多様体を、有理多様体(rational variety)と言う。有理多様体は、代数多様体上の函数体が、ある不定元の集合 の有理函数の体 に同型であることを意味する。ここの d は、(dimension of an algebraic variety)である。 (ja) 대수기하학에서 유리 다양체(有理多樣體, 영어: rational variety)는 사영 공간과 쌍유리 동치인 대수다양체이다. (ko) 在數學中的代數幾何領域，域 上的有理簇是一個雙有理等價於射影空間 （）的代數簇。有理性僅依賴於其函數域，更明確地說，代數簇 是有理簇若且唯若 ，其中 是獨立的變元。 (zh) |
| rdfs:label |
Variété rationnelle (fr) 유리 다양체 (ko) 有理多様体 (ja) Rational variety (en) 有理簇 (zh) |
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