About: Quadric (algebraic geometry)

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In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine space. An example is the quadric surface in projective space over the complex numbers C. A quadric has a natural action of the orthogonal group, and so the study of quadrics can be considered as a descendant of Euclidean geometry.

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rdfs:label	Quadric (algebraic geometry) (en)
rdfs:comment	In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine space. An example is the quadric surface in projective space over the complex numbers C. A quadric has a natural action of the orthogonal group, and so the study of quadrics can be considered as a descendant of Euclidean geometry. (en)
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dcterms:subject	Projective geometry Algebraic geometry Algebraic homogeneous spaces Quadrics
Wikipage page ID	64926134 (xsd:integer)
Wikipage revision ID	1071699768 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective space Rational variety Nondegenerate bilinear form Determinant Algebraic K-theory Derived category Intersection Compact Lie group Complex number Mathematics Chow ring Grassmannian Connected space Lagrangian Grassmannian Chow group Stereographic projection Spin group Symplectic group Maximal compact subgroup Coherent sheaves Irreducible polynomial Fano varieties Linear algebraic group Semisimple algebraic group Algebraic geometry Algebraic varieties Projective geometry Field (mathematics) Equivariant Projective cone Quadratic form Rank (linear algebra) Rational function Rational point Reflection (mathematics) Hyperplane Topological K-theory Algebraic geometry Algebraic homogeneous spaces Characteristic (algebra) Chern class Coherent sheaf Cohomology Hessian matrix Hodge theory Homogeneous polynomial Polynomial Special orthogonal group Spin representation Split reductive group Quadrics Free abelian group Exceptional collection Schubert varieties Algebraically closed Bruhat decomposition Orthogonal group Real number Scheme (mathematics) Segre embedding Singular homology Unitary group Veronese embedding Triality Euclidean geometry Mikhail Kapranov Algebraic vector bundle Smooth scheme Richard Swan Simply connected Springer-Verlag Parabolic subgroup Symplectic form Conic Projective homogeneous varieties Projective homogeneous variety
sameAs	Quadric (algebraic geometry) Quadric (algebraic geometry)
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has abstract	In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine space. An example is the quadric surface in projective space over the complex numbers C. A quadric has a natural action of the orthogonal group, and so the study of quadrics can be considered as a descendant of Euclidean geometry. Many properties of quadrics hold more generally for projective homogeneous varieties. Another generalization of quadrics is provided by Fano varieties. (en)
prov:wasDerivedFrom	wikipedia-en:Quadric_(algebraic_geometry)?oldid=1071699768&ns=0
page length (characters) of wiki page	21110 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Quadric_(algebraic_geometry)
is Link from a Wikipage to another Wikipage of	List of algebraic geometry topics Julius Plücker

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