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- Complete_intersection abstract "In mathematics, an algebraic variety V in projective space is a complete intersection if the ideal of V is generated by exactly codim V elements. That is, if V has dimension m and lies in projective space Pn, there should exist n − m homogeneous polynomials Fi(X0, ..., Xn), 1 ≤ i ≤ n − m,in the homogeneous coordinates Xj, which generate all other homogeneous polynomials that vanish on V.Geometrically, each Fi defines a hypersurface; the intersection of these hypersurfaces should be V. The intersection of n-m hypersurfaces will always have dimension at least m, assuming that the field of scalars is an algebraically closed field such as the complex numbers. The question is essentially, can we get the dimension down to m, with no extra points in the intersection? This condition is fairly hard to check as soon as the codimension n − m ≥ 2. When n − m = 1 then V is automatically a hypersurface and there is nothing to prove.".
- Complete_intersection wikiPageExternalLink Complete_intersections.
- Complete_intersection wikiPageID "3116835".
- Complete_intersection wikiPageLength "4801".
- Complete_intersection wikiPageOutDegree "29".
- Complete_intersection wikiPageRevisionID "678977511".
- Complete_intersection wikiPageWikiLink Algebraic_variety.
- Complete_intersection wikiPageWikiLink Algebraically_closed_field.
- Complete_intersection wikiPageWikiLink Bxc3xa9zouts_theorem.
- Complete_intersection wikiPageWikiLink Category:Algebraic_geometry.
- Complete_intersection wikiPageWikiLink Category:Commutative_algebra.
- Complete_intersection wikiPageWikiLink Commutative_algebra.
- Complete_intersection wikiPageWikiLink Complete_intersection_ring.
- Complete_intersection wikiPageWikiLink Complex_number.
- Complete_intersection wikiPageWikiLink Cubic_surface.
- Complete_intersection wikiPageWikiLink Degree_of_an_algebraic_variety.
- Complete_intersection wikiPageWikiLink Dimension_of_an_algebraic_variety.
- Complete_intersection wikiPageWikiLink Elliptic_curve.
- Complete_intersection wikiPageWikiLink General_position.
- Complete_intersection wikiPageWikiLink Graded_ring.
- Complete_intersection wikiPageWikiLink Hodge_theory.
- Complete_intersection wikiPageWikiLink Homogeneous_coordinates.
- Complete_intersection wikiPageWikiLink Hypersurface.
- Complete_intersection wikiPageWikiLink Kunihiko_Kodaira.
- Complete_intersection wikiPageWikiLink Localization_of_a_ring.
- Complete_intersection wikiPageWikiLink Multiset.
- Complete_intersection wikiPageWikiLink Projective_space.
- Complete_intersection wikiPageWikiLink Quadric.
- Complete_intersection wikiPageWikiLink Radical_of_an_ideal.
- Complete_intersection wikiPageWikiLink Regular_sequence.
- Complete_intersection wikiPageWikiLink Scheme_(mathematics).
- Complete_intersection wikiPageWikiLink Tangent_space.
- Complete_intersection wikiPageWikiLink Transversality_(mathematics).
- Complete_intersection wikiPageWikiLink Tuple.
- Complete_intersection wikiPageWikiLink Twisted_cubic.
- Complete_intersection wikiPageWikiLinkText "Complete intersection".
- Complete_intersection wikiPageWikiLinkText "complete intersection".
- Complete_intersection wikiPageUsesTemplate Template:Citation.
- Complete_intersection wikiPageUsesTemplate Template:For.
- Complete_intersection subject Category:Algebraic_geometry.
- Complete_intersection subject Category:Commutative_algebra.
- Complete_intersection hypernym Intersection.
- Complete_intersection type RoadJunction.
- Complete_intersection comment "In mathematics, an algebraic variety V in projective space is a complete intersection if the ideal of V is generated by exactly codim V elements. That is, if V has dimension m and lies in projective space Pn, there should exist n − m homogeneous polynomials Fi(X0, ..., Xn), 1 ≤ i ≤ n − m,in the homogeneous coordinates Xj, which generate all other homogeneous polynomials that vanish on V.Geometrically, each Fi defines a hypersurface; the intersection of these hypersurfaces should be V.".
- Complete_intersection label "Complete intersection".
- Complete_intersection sameAs Q5156502.
- Complete_intersection sameAs m.08shyw.
- Complete_intersection sameAs Q5156502.
- Complete_intersection wasDerivedFrom Complete_intersection?oldid=678977511.
- Complete_intersection isPrimaryTopicOf Complete_intersection.