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Complete intersection

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:

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Map overview Semantic statistics

Complete intersection

Nodes39
Edges38
Triples63
Avg. degree1.95
Density0.051282
Components1

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Complete intersection

Top relations

related to References · 29
Complete intersection → Algebraic Geometry, Bestiary, Calabi-Yau Manifolds, Cambridge, Cambridge University Press, CBO9780511662720, Characteristics, Christian, Complete Intersections, Fields Institute Monographs, First Course, Harris, Hübsch, ISBN, Isolated, Joe, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, London Mathematical Society Lecture
related to Twisted cubic · 8
Complete intersection → Gamma, If, Note, One, Proj, Span, Veronese, We
related to General position · 6
Complete intersection → Fi, For, In, The, X0, Xn
related to Homology · 6
Complete intersection → CP, Euler, In, Lefschetz, Since, This
related to Examples · 3
Complete intersection → Easy, For, It
related to Multidegree · 3
Complete intersection → For, Kunihiko Kodaira, The Hodge
related to Union of varieties differing in dimension · 3
Complete intersection → Another, For, It
related to Euler characteristic · 2
Complete intersection → Hirzebruch, It
related to External links · 2
Complete intersection → Complete, Manifold Atlas

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Important terminology

intersection complete dimension intersections displaystyle hypersurfaces projective space isbn example mathbb hypersurface two local ideal points condition examples twisted cubic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the complex numbersinstance ofassuming that the field of scalars is an algebraically closed field0.80text
Complete intersectionrelated to Euler characteristicHirzebruch0.60section
Complete intersectionrelated to Euler characteristicIt0.60section
Complete intersectionrelated to ExamplesEasy0.60section
Complete intersectionrelated to ExamplesFor0.60section
Complete intersectionrelated to ExamplesIt0.60section
Complete intersectionrelated to External linksComplete0.60section
Complete intersectionrelated to External linksManifold Atlas0.60section
Complete intersectionrelated to General positionFor0.60section
Complete intersectionrelated to General positionThe0.60section
Complete intersectionrelated to General positionFi0.60section
Complete intersectionrelated to General positionX00.60section

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