| 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) |
| dbo:wikiPageExternalLink |
http://www.cambridge.org/catalogue/catalogue.asp%3Fisbn=9780521832076 |
| dbo:wikiPageID |
865939 (xsd:integer) |
| dbo:wikiPageLength |
11909 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1124321490 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Cambridge_University_Press dbr:Projective_space dbc:Algebraic_varieties dbr:Annals_of_Mathematics dbr:Cubic_surface dbr:Indeterminate_(variable) dbr:Intermediate_Jacobian dbr:Mathematics dbr:Galois_theory dbr:Arithmetic_genus dbr:Function_field_of_an_algebraic_variety dbr:Mathematische_Annalen dbr:Matematicheskii_Sbornik dbr:Quartic_threefold dbr:Rational_surface dbr:Riemann–Hurwitz_formula dbr:Algebraic_variety dbr:Field_(mathematics) dbr:Fixed_point_(mathematics) dbr:Dimension_of_an_algebraic_variety dbr:Projective_line dbr:Rational_function dbr:Regular_map_(algebraic_geometry) dbr:Group_action_(mathematics) dbr:Isomorphic dbr:Hypersurface dbc:Field_(mathematics) dbc:Birational_geometry dbr:János_Kollár dbr:Birational_geometry dbr:Jacob_Lüroth dbr:Moduli_space dbr:Field_extension dbr:Onto dbr:Rational_curve dbr:Finite_group dbr:Severi–Brauer_variety dbr:Transcendence_degree dbr:Zariski_surface dbr:Plurigenus dbr:Affine_algebraic_variety dbr:Springer-Verlag dbr:Castelnuovo's_theorem dbr:Field_homomorphism dbr:Rational_function_field dbr:Rational_map dbr:Path_connectedness dbr:Purely_transcendental dbr:Three-fold dbr:Degree_(algebraic_geometry) dbr:Genus_of_a_curve dbr:Birationally_equivalent dbr:Cubic_hypersurface |
| dbp:authorlink |
Richard Swan (en) |
| dbp:first |
R. G. (en) |
| dbp:last |
Swan (en) |
| dbp:wikiPageUsesTemplate |
dbt:Citation dbt:Harv dbt:Harvtxt dbt:Main dbt:Reflist dbt:Vanchor dbt:Harvs |
| dbp:year |
1969 (xsd:integer) |
| dct:subject |
dbc:Algebraic_varieties dbc:Field_(mathematics) dbc:Birational_geometry |
| rdf:type |
yago:Abstraction100002137 yago:Assortment108398773 yago:Collection107951464 yago:Group100031264 yago:WikicatAlgebraicVarieties |
| 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) |
| owl:sameAs |
freebase:Rational variety yago-res:Rational variety wikidata:Rational variety dbpedia-fr:Rational variety dbpedia-ja:Rational variety dbpedia-ko:Rational variety dbpedia-zh:Rational variety https://global.dbpedia.org/id/3H7NL |
| prov:wasDerivedFrom |
wikipedia-en:Rational_variety?oldid=1124321490&ns=0 |
| foaf:isPrimaryTopicOf |
wikipedia-en:Rational_variety |
| is dbo:wikiPageRedirects of |
dbr:Noether's_problem dbr:Noether_problem dbr:Unirationality dbr:Rational_parametrization dbr:Rationally_connected_variety dbr:Luroth's_problem dbr:Lueroth's_problem dbr:Lueroth's_theorem dbr:Rational_varieties dbr:Rationality_question dbr:Lüroth's_Theorem dbr:Lüroth's_problem dbr:Lüroth_problem dbr:Lüroth’s_theorem dbr:Unirational dbr:Unirational_variety |
| is dbo:wikiPageWikiLink of |
dbr:List_of_University_of_Utah_people dbr:List_of_algebraic_geometry_topics dbr:List_of_complex_and_algebraic_surfaces dbr:Noether's_problem dbr:Noether_problem dbr:Cubic_surface dbr:Unirationality dbr:Intermediate_Jacobian dbr:Quadric_(algebraic_geometry) dbr:Glossary_of_algebraic_geometry dbr:Glossary_of_classical_algebraic_geometry dbr:Cone_of_curves dbr:Stereographic_projection dbr:Segre_cubic dbr:Linear_algebraic_group dbr:Rational_surface dbr:Algebraic_geometry dbr:Barth–Nieto_quintic dbr:Fano_variety dbr:Projective_line dbr:Rational_point dbr:Gröbner_basis dbr:Herbert_Clemens dbr:Jessen's_icosahedron dbr:János_Kollár dbr:Birational_geometry dbr:Burkhardt_quartic dbr:Kodaira_dimension dbr:Rational_parametrization dbr:Rationally_connected_variety dbr:Klein_cubic_threefold dbr:Ruled_variety dbr:Luroth's_problem dbr:Siegel_modular_variety dbr:Lueroth's_problem dbr:Lueroth's_theorem dbr:Rational_varieties dbr:Rationality_question dbr:Lüroth's_Theorem dbr:Lüroth's_problem dbr:Lüroth_problem dbr:Lüroth’s_theorem dbr:Unirational dbr:Unirational_variety |
| is foaf:primaryTopic of |
wikipedia-en:Rational_variety |
