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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 wikiPageRevisionID "590176908".
- Homogeneous_coordinate_ring hasPhotoCollection Homogeneous_coordinate_ring.
- Homogeneous_coordinate_ring subject Category:Algebraic_varieties.
- Homogeneous_coordinate_ring type Abstraction100002137.
- Homogeneous_coordinate_ring type AlgebraicVarieties.
- Homogeneous_coordinate_ring type Assortment108398773.
- Homogeneous_coordinate_ring type Collection107951464.
- Homogeneous_coordinate_ring type Group100031264.
- 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 m.06_xdxl.
- Homogeneous_coordinate_ring sameAs Q5891327.
- Homogeneous_coordinate_ring sameAs Q5891327.
- Homogeneous_coordinate_ring sameAs Homogeneous_coordinate_ring.
- Homogeneous_coordinate_ring wasDerivedFrom Homogeneous_coordinate_ring?oldid=590176908.
- Homogeneous_coordinate_ring isPrimaryTopicOf Homogeneous_coordinate_ring.