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MultiprojectiveVarieties :: MultirationalMap ** Ring

MultirationalMap ** Ring -- change the coefficient ring of a multi-rational map

Synopsis

Description

It is necessary that all multi-forms in the old coefficient ring F can be automatically coerced into the new coefficient ring K.

i1 : Phi = inverse first graph rationalMap PP_QQ^(2,2);

o1 : MultirationalMap (birational map from PP^5 to 5-dimensional subvariety of PP^5 x PP^5)
 
i2 : describe Phi

o2 = multi-rational map consisting of 2 rational maps
     source variety: PP^5
     target variety: 5-dimensional subvariety of PP^5 x PP^5 cut out by 8 hypersurfaces of multi-degree (1,1)
     base locus: surface in PP^5 cut out by 6 hypersurfaces of degree 2
     dominance: true
     multidegree: {1, 3, 9, 23, 51, 102}
     degree: 1
     degree sequence (map 1/2): [1]
     degree sequence (map 2/2): [2]
     coefficient ring: QQ
 
i3 : K = ZZ/65521;
 
i4 : Phi' = Phi ** K;

o4 : MultirationalMap (birational map from PP^5 to 5-dimensional subvariety of PP^5 x PP^5)
 
i5 : describe Phi'

o5 = multi-rational map consisting of 2 rational maps
     source variety: PP^5
     target variety: 5-dimensional subvariety of PP^5 x PP^5 cut out by 8 hypersurfaces of multi-degree (1,1)
     base locus: surface in PP^5 cut out by 6 hypersurfaces of degree 2
     dominance: true
     multidegree: {1, 3, 9, 23, 51, 102}
     degree: 1
     degree sequence (map 1/2): [1]
     degree sequence (map 2/2): [2]
     coefficient ring: K
 
i6 : Phi'' = Phi ** frac(K[t]);

o6 : MultirationalMap (birational map from PP^5 to 5-dimensional subvariety of PP^5 x PP^5)
 
i7 : describe Phi''

o7 = multi-rational map consisting of 2 rational maps
     source variety: PP^5
     target variety: 5-dimensional subvariety of PP^5 x PP^5 cut out by 8 hypersurfaces of multi-degree (1,1)
     base locus: surface in PP^5 cut out by 6 hypersurfaces of degree 2
     dominance: true
     multidegree: {1, 3, 9, 23, 51, 102}
     degree: 1
     degree sequence (map 1/2): [1]
     degree sequence (map 2/2): [2]
     coefficient ring: frac(K[t])

See also