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MultiprojectiveVarieties :: MultirationalMap || MultiprojectiveVariety

MultirationalMap || MultiprojectiveVariety -- restriction of a multi-rational map

Synopsis

Description

i1 : ZZ/33331[x_0..x_3], f = rationalMap {x_2^2-x_1*x_3,x_1*x_2-x_0*x_3,x_1^2-x_0*x_2}, g = rationalMap {x_2^2-x_1*x_3,x_1*x_2-x_0*x_3};
i2 : Phi = last graph rationalMap {f,g};

o2 : MultirationalMap (rational map from threefold in PP^3 x PP^2 x PP^1 to PP^2 x PP^1)
i3 : Z = projectiveVariety ideal random({1,2},ring target Phi);

o3 : ProjectiveVariety, surface in PP^2 x PP^1
i4 : Phi' = Phi||Z;

o4 : MultirationalMap (rational map from surface in PP^3 x PP^2 x PP^1 to Z)
i5 : target Phi'

o5 = Z

o5 : ProjectiveVariety, surface in PP^2 x PP^1
i6 : assert(source Phi' == Phi^* Z)

The following is a shortcut to take restrictions on random hypersurfaces as above.

i7 : Phi||{1,2};

o7 : MultirationalMap (rational map from surface in PP^3 x PP^2 x PP^1 to surface in PP^2 x PP^1)

See also