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- Homogeneous_coordinate_ring abstract "In algebraic geometry, the homogeneous coordinate ring R of an algebraic variety V given as a subvariety of projective space of a given dimension N is by definition the quotient ringR = K[X0, X1, X2, ..., XN]/Iwhere I is the homogeneous ideal defining V, K is the algebraically closed field over which V is defined, andK[X0, X1, X2, ..., XN]is the polynomial ring in N + 1 variables Xi. The polynomial ring is therefore the homogeneous coordinate ring of the projective space itself, and the variables are the homogeneous coordinates, for a given choice of basis (in the vector space underlying the projective space). The choice of basis means this definition is not intrinsic, but it can be made so by using the symmetric algebra.".
- Homogeneous_coordinate_ring wikiPageID "23833909".
- Homogeneous_coordinate_ring wikiPageLength "8491".
- Homogeneous_coordinate_ring wikiPageOutDegree "58".
- Homogeneous_coordinate_ring wikiPageRevisionID "674543380".
- Homogeneous_coordinate_ring wikiPageWikiLink Algebraic_geometry.
- Homogeneous_coordinate_ring wikiPageWikiLink Algebraic_variety.
- Homogeneous_coordinate_ring wikiPageWikiLink Algebraically_closed_field.
- Homogeneous_coordinate_ring wikiPageWikiLink Ample_line_bundle.
- Homogeneous_coordinate_ring wikiPageWikiLink Canonical_bundle.
- Homogeneous_coordinate_ring wikiPageWikiLink Canonical_curve.
- Homogeneous_coordinate_ring wikiPageWikiLink Castelnuovo–Mumford_regularity.
- Homogeneous_coordinate_ring wikiPageWikiLink Category:Algebraic_varieties.
- Homogeneous_coordinate_ring wikiPageWikiLink Chain_complex.
- Homogeneous_coordinate_ring wikiPageWikiLink Complete_intersection.
- Homogeneous_coordinate_ring wikiPageWikiLink Complete_linear_system.
- Homogeneous_coordinate_ring wikiPageWikiLink David_Hilbert.
- Homogeneous_coordinate_ring wikiPageWikiLink Direct_sum.
- Homogeneous_coordinate_ring wikiPageWikiLink Direct_summand.
- Homogeneous_coordinate_ring wikiPageWikiLink Divisors_of_zero.
- Homogeneous_coordinate_ring wikiPageWikiLink Eagon–Northcott_complex.
- Homogeneous_coordinate_ring wikiPageWikiLink Elimination_theory.
- Homogeneous_coordinate_ring wikiPageWikiLink Elliptic_curve.
- Homogeneous_coordinate_ring wikiPageWikiLink Equations_defining_abelian_varieties.
- Homogeneous_coordinate_ring wikiPageWikiLink Free_module.
- Homogeneous_coordinate_ring wikiPageWikiLink Free_resolution.
- Homogeneous_coordinate_ring wikiPageWikiLink Graded_module.
- Homogeneous_coordinate_ring wikiPageWikiLink Graded_ring.
- Homogeneous_coordinate_ring wikiPageWikiLink Gröbner_bases.
- Homogeneous_coordinate_ring wikiPageWikiLink Gröbner_basis.
- Homogeneous_coordinate_ring wikiPageWikiLink Guido_Castelnuovo.
- Homogeneous_coordinate_ring wikiPageWikiLink Hilbert_polynomial.
- Homogeneous_coordinate_ring wikiPageWikiLink Hilbert_series_and_Hilbert_polynomial.
- Homogeneous_coordinate_ring wikiPageWikiLink Hilberts_Nullstellensatz.
- Homogeneous_coordinate_ring wikiPageWikiLink Homogeneous_coordinates.
- Homogeneous_coordinate_ring wikiPageWikiLink Homogeneous_ideal.
- Homogeneous_coordinate_ring wikiPageWikiLink Homological_algebra.
- Homogeneous_coordinate_ring wikiPageWikiLink Hypersurface.
- Homogeneous_coordinate_ring wikiPageWikiLink Integral_domain.
- Homogeneous_coordinate_ring wikiPageWikiLink Integrally_closed.
- Homogeneous_coordinate_ring wikiPageWikiLink Invertible_sheaf.
- Homogeneous_coordinate_ring wikiPageWikiLink Irreducible_algebraic_set.
- Homogeneous_coordinate_ring wikiPageWikiLink Irreducible_component.
- Homogeneous_coordinate_ring wikiPageWikiLink Linear_normality.
- Homogeneous_coordinate_ring wikiPageWikiLink Linear_projection.
- Homogeneous_coordinate_ring wikiPageWikiLink Linear_system_of_divisors.
- Homogeneous_coordinate_ring wikiPageWikiLink Mapping_cone_(homological_algebra).
- Homogeneous_coordinate_ring wikiPageWikiLink Mapping_cone_of_complexes.
- Homogeneous_coordinate_ring wikiPageWikiLink Nakayama_lemma.
- Homogeneous_coordinate_ring wikiPageWikiLink Nakayamas_lemma.
- Homogeneous_coordinate_ring wikiPageWikiLink Nilpotent.
- Homogeneous_coordinate_ring wikiPageWikiLink Nilpotent_element.
- Homogeneous_coordinate_ring wikiPageWikiLink Non-singular.
- Homogeneous_coordinate_ring wikiPageWikiLink Normal_scheme.
- Homogeneous_coordinate_ring wikiPageWikiLink Normal_variety.
- Homogeneous_coordinate_ring wikiPageWikiLink Oscar_Zariski.
- Homogeneous_coordinate_ring wikiPageWikiLink Pierre_Samuel.
- Homogeneous_coordinate_ring wikiPageWikiLink Polynomial_ring.
- Homogeneous_coordinate_ring wikiPageWikiLink Prime_ideal.
- Homogeneous_coordinate_ring wikiPageWikiLink Proj_construction.
- Homogeneous_coordinate_ring wikiPageWikiLink Projection_(linear_algebra).
- Homogeneous_coordinate_ring wikiPageWikiLink Projective_Nullstellensatz.
- Homogeneous_coordinate_ring wikiPageWikiLink Projective_space.
- Homogeneous_coordinate_ring wikiPageWikiLink Projective_variety.
- Homogeneous_coordinate_ring wikiPageWikiLink Quotient_ring.
- Homogeneous_coordinate_ring wikiPageWikiLink Rational_normal_curve.
- Homogeneous_coordinate_ring wikiPageWikiLink Resolution_(algebra).
- Homogeneous_coordinate_ring wikiPageWikiLink Scheme_(mathematics).
- Homogeneous_coordinate_ring wikiPageWikiLink Scheme_theory.
- Homogeneous_coordinate_ring wikiPageWikiLink Serre_twist_sheaf.
- Homogeneous_coordinate_ring wikiPageWikiLink Singular_point_of_an_algebraic_variety.
- Homogeneous_coordinate_ring wikiPageWikiLink Subvariety.
- Homogeneous_coordinate_ring wikiPageWikiLink Symmetric_algebra.
- Homogeneous_coordinate_ring wikiPageWikiLink Syzygy_(mathematics).
- Homogeneous_coordinate_ring wikiPageWikiLink Tautological_bundle.
- Homogeneous_coordinate_ring wikiPageWikiLink Tautological_line_bundle.
- Homogeneous_coordinate_ring wikiPageWikiLink Up_to.
- Homogeneous_coordinate_ring wikiPageWikiLink Vector_space.
- Homogeneous_coordinate_ring wikiPageWikiLink Veronese_mapping.
- Homogeneous_coordinate_ring wikiPageWikiLink Veronese_surface.
- Homogeneous_coordinate_ring wikiPageWikiLink Very_ample_line_bundle.
- Homogeneous_coordinate_ring wikiPageWikiLink Zero_divisor.
- Homogeneous_coordinate_ring wikiPageWikiLinkText "Homogeneous coordinate ring".
- Homogeneous_coordinate_ring wikiPageWikiLinkText "coordinate ring".
- Homogeneous_coordinate_ring wikiPageWikiLinkText "homogeneous coordinate ring".
- Homogeneous_coordinate_ring wikiPageWikiLinkText "homogeneous coordinate ring#Projective normality".
- Homogeneous_coordinate_ring hasPhotoCollection Homogeneous_coordinate_ring.
- Homogeneous_coordinate_ring wikiPageUsesTemplate Template:Reflist.
- Homogeneous_coordinate_ring subject Category:Algebraic_varieties.
- Homogeneous_coordinate_ring hypernym V.
- Homogeneous_coordinate_ring type MeanOfTransportation.
- Homogeneous_coordinate_ring type Variety.
- Homogeneous_coordinate_ring comment "In algebraic geometry, the homogeneous coordinate ring R of an algebraic variety V given as a subvariety of projective space of a given dimension N is by definition the quotient ringR = K[X0, X1, X2, ..., XN]/Iwhere I is the homogeneous ideal defining V, K is the algebraically closed field over which V is defined, andK[X0, X1, X2, ..., XN]is the polynomial ring in N + 1 variables Xi.".
- Homogeneous_coordinate_ring label "Homogeneous coordinate ring".
- Homogeneous_coordinate_ring sameAs 斉次座標環.
- Homogeneous_coordinate_ring sameAs m.06_xdxl.
- Homogeneous_coordinate_ring sameAs Q5891327.
- Homogeneous_coordinate_ring sameAs Q5891327.
- Homogeneous_coordinate_ring wasDerivedFrom Homogeneous_coordinate_ring?oldid=674543380.
- Homogeneous_coordinate_ring isPrimaryTopicOf Homogeneous_coordinate_ring.