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- Complete_variety abstract "In mathematics, in particular in algebraic geometry, a complete algebraic variety is an algebraic variety X, such that for any variety Y the projection morphismX × Y → Yis a closed map, i.e. maps closed sets onto closed sets. This can be seen as an analogue of compactness in algebraic geometry: a topological space X is compact if and only if projection along X is a closed map in any product X × Y, equipped with product topology.The image of a complete variety is closed and is a complete variety. A closed subvariety of a complete variety is complete.A complex variety is complete if and only if it is compact as a complex-analytic variety.The most common example of a complete variety is a projective variety, but there do exist complete non-projective varieties in dimensions 2 and higher. The first examples of non-projective complete varieties were given by Masayoshi Nagata and Heisuke Hironaka. An affine space of positive dimension is not complete.The morphism taking a complete variety to a point is a proper morphism, in the sense of scheme theory. An intuitive justification of 'complete', in the sense of 'no missing points', can be given on the basis of the valuative criterion of properness, which goes back to Claude Chevalley.".
- Complete_variety wikiPageExternalLink ag.html.
- Complete_variety wikiPageID "1047627".
- Complete_variety wikiPageLength "2596".
- Complete_variety wikiPageOutDegree "23".
- Complete_variety wikiPageRevisionID "677879596".
- Complete_variety wikiPageWikiLink Affine_space.
- Complete_variety wikiPageWikiLink Algebraic_geometry.
- Complete_variety wikiPageWikiLink Algebraic_variety.
- Complete_variety wikiPageWikiLink Category:Algebraic_varieties.
- Complete_variety wikiPageWikiLink Chows_lemma.
- Complete_variety wikiPageWikiLink Claude_Chevalley.
- Complete_variety wikiPageWikiLink Closed_map.
- Complete_variety wikiPageWikiLink Closed_set.
- Complete_variety wikiPageWikiLink Compact_space.
- Complete_variety wikiPageWikiLink Complex-analytic_variety.
- Complete_variety wikiPageWikiLink Dimension_of_an_algebraic_variety.
- Complete_variety wikiPageWikiLink Fano_variety.
- Complete_variety wikiPageWikiLink Heisuke_Hironaka.
- Complete_variety wikiPageWikiLink Masayoshi_Nagata.
- Complete_variety wikiPageWikiLink Mathematics.
- Complete_variety wikiPageWikiLink Morphism_of_algebraic_varieties.
- Complete_variety wikiPageWikiLink Open_and_closed_maps.
- Complete_variety wikiPageWikiLink Product_(category_theory).
- Complete_variety wikiPageWikiLink Projective_variety.
- Complete_variety wikiPageWikiLink Proper_morphism.
- Complete_variety wikiPageWikiLink Regular_map_(algebraic_geometry).
- Complete_variety wikiPageWikiLink Scheme_(mathematics).
- Complete_variety wikiPageWikiLink Scheme_theory.
- Complete_variety wikiPageWikiLink Springer-Verlag.
- Complete_variety wikiPageWikiLink Springer_Science+Business_Media.
- Complete_variety wikiPageWikiLink Theorem_of_the_cube.
- Complete_variety wikiPageWikiLink Valuative_criterion_of_properness.
- Complete_variety wikiPageWikiLinkText "Complete variety".
- Complete_variety wikiPageWikiLinkText "complete varieties".
- Complete_variety wikiPageWikiLinkText "complete variety".
- Complete_variety wikiPageWikiLinkText "complete".
- Complete_variety wikiPageWikiLinkText "non-complete".
- Complete_variety wikiPageWikiLinkText "proper".
- Complete_variety hasPhotoCollection Complete_variety.
- Complete_variety wikiPageUsesTemplate Template:Citation.
- Complete_variety wikiPageUsesTemplate Template:Citation_needed.
- Complete_variety wikiPageUsesTemplate Template:Hartshorne_AG.
- Complete_variety wikiPageUsesTemplate Template:Reflist.
- Complete_variety subject Category:Algebraic_varieties.
- Complete_variety hypernym X.
- Complete_variety type Article.
- Complete_variety type Work.
- Complete_variety type Article.
- Complete_variety type Variety.
- Complete_variety comment "In mathematics, in particular in algebraic geometry, a complete algebraic variety is an algebraic variety X, such that for any variety Y the projection morphismX × Y → Yis a closed map, i.e. maps closed sets onto closed sets.".
- Complete_variety label "Complete variety".
- Complete_variety sameAs m.041d3m.
- Complete_variety sameAs Komplett_varietet.
- Complete_variety sameAs Q5156516.
- Complete_variety sameAs Q5156516.
- Complete_variety wasDerivedFrom Complete_variety?oldid=677879596.
- Complete_variety isPrimaryTopicOf Complete_variety.