About: Plücker embedding

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In mathematics, the Plücker map embeds the Grassmannian , whose elements are k-dimensional subspaces of an n-dimensional vector space V, in a projective space, thereby realizing it as an algebraic variety. More precisely, the Plücker map embeds into the projectivization of the -th exterior power of . The image is algebraic, consisting of the intersection of a number of quadrics defined by the Plücker relations (see below).

Attributes	Values
rdf:type	software
rdfs:label	Graßmann-Plücker-Relation (de) Coordonnées grassmanniennes (fr) Plücker embedding (en)
rdfs:comment	Die Graßmann-Plücker-Relationen beschreiben Beziehungen zwischen Determinanten mit teilweise übereinstimmenden Spalten. (de) Les coordonnées grassmanniennes sont une généralisation des coordonnées plückeriennes qui permettent de paramétrer les sous espaces de dimension de l'espace vectoriel par un élément de l'espace projectif de l'espace vectoriel des produits extérieurs des familles de vecteurs de . (fr) In mathematics, the Plücker map embeds the Grassmannian , whose elements are k-dimensional subspaces of an n-dimensional vector space V, in a projective space, thereby realizing it as an algebraic variety. More precisely, the Plücker map embeds into the projectivization of the -th exterior power of . The image is algebraic, consisting of the intersection of a number of quadrics defined by the Plücker relations (see below). (en)
dcterms:subject	Differential geometry Algebraic geometry
Wikipage page ID	1190270 (xsd:integer)
Wikipage revision ID	1039374073 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective space Algebraic independence Julius Plücker Vector space Differential geometry Mathematics Grassmannian Bracket ring Linear algebra Embedding Linear subspace Algebraic variety Exterior power Field (mathematics) Dimension (vector space) Projective line Hermann Grassmann Algebraic geometry Klein quadric Plücker coordinates Springer-Verlag
sameAs	Plücker embedding Plücker embedding Plücker embedding Plücker embedding Plücker embedding
dbp:wikiPageUsesTemplate	dbt:= dbt:Cite_book dbt:Math dbt:Mvar dbt:NumBlk dbt:Reflist dbt:EquationRef dbt:EquationNote
has abstract	Die Graßmann-Plücker-Relationen beschreiben Beziehungen zwischen Determinanten mit teilweise übereinstimmenden Spalten. (de) Les coordonnées grassmanniennes sont une généralisation des coordonnées plückeriennes qui permettent de paramétrer les sous espaces de dimension de l'espace vectoriel par un élément de l'espace projectif de l'espace vectoriel des produits extérieurs des familles de vecteurs de . (fr) In mathematics, the Plücker map embeds the Grassmannian , whose elements are k-dimensional subspaces of an n-dimensional vector space V, in a projective space, thereby realizing it as an algebraic variety. More precisely, the Plücker map embeds into the projectivization of the -th exterior power of . The image is algebraic, consisting of the intersection of a number of quadrics defined by the Plücker relations (see below). The Plücker embedding was first defined by Julius Plücker in the case as a way of describing the lines in three-dimensional space (which, as projective lines in real projective space, correspond to two-dimensional subspaces of a four-dimensional vector space). The image of that embedding is the Klein quadric in RP5. Hermann Grassmann generalized Plücker's embedding to arbitrary k and n. The homogeneous coordinates of the image of the Grassmannian under the Plücker embedding, relative to the basis in the exterior space corresponding to the natural basis in (where is the base field) are called Plücker coordinates. (en)
gold:hypernym	Method
prov:wasDerivedFrom	wikipedia-en:Plücker_embedding?oldid=1039374073&ns=0
page length (characters) of wiki page	6751 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Plücker_embedding
is Link from a Wikipage to another Wikipage of	Hodge star operator Julius Plücker Integrable system Geometric algebra Glossary of algebraic geometry Grassmannian Bracket ring Plucker embedding Pluecker embedding Chow variety Plücker matrix K-stability Local twistor Algebraic variety Exterior algebra Grassmann bundle Projective variety Hermann Grassmann Homogeneous coordinates Bombieri norm Grassmann coordinates Grassmann coordinates. Graßmann-Plücker relation Graßmann-Plücker relations Graßmann–Plücker relation Graßmann–Plücker relations Twistor space List of things named after Hermann Grassmann Quasideterminant Plücker relations Plucker imbedding Plucker relations Plücker imbedding
is Wikipage redirect of	Plucker embedding Pluecker embedding Grassmann coordinates Grassmann coordinates. Graßmann-Plücker relation Graßmann-Plücker relations Graßmann–Plücker relation Graßmann–Plücker relations Plücker relations Plucker imbedding Plucker relations Plücker imbedding
is known for of	Julius Plücker
is known for of	Julius Plücker
is foaf:primaryTopic of	wikipedia-en:Plücker_embedding

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