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MultiprojectiveVarieties :: MultiprojectiveVariety ** MultiprojectiveVariety

MultiprojectiveVariety ** MultiprojectiveVariety -- product of projective varieties

Synopsis

Description

i1 : R = ZZ/101[x_0..x_2,y_0,y_1,Degrees=>{3:{1,0},2:{0,1}}];
i2 : S = ZZ/101[x_0,x_1,y_0..y_2,z_0,z_1,Degrees=>{2:{1,0,0},3:{0,1,0},2:{0,0,1}}];
i3 : X = projectiveVariety ideal(random({2,1},R),random({1,1},R));

o3 : ProjectiveVariety, curve in PP^2 x PP^1
i4 : Y = projectiveVariety ideal random({1,1,1},S);

o4 : ProjectiveVariety, hypersurface in PP^1 x PP^2 x PP^1
i5 : XxY = X ** Y;

o5 : ProjectiveVariety, 4-dimensional subvariety of PP^2 x PP^1 x PP^1 x PP^2 x PP^1
i6 : describe X

o6 = ambient:.............. PP^2 x PP^1
     dim:.................. 1
     codim:................ 2
     degree:............... 5
     multidegree:.......... 2*T_0^2+3*T_0*T_1
     generators:........... (1,1)^1 (3,0)^1 (2,1)^1 
     purity:............... true
     dim sing. l.:......... -1
     Segre embedding:...... map to PP^4 ⊂ PP^5
i7 : describe Y

o7 = ambient:.............. PP^1 x PP^2 x PP^1
     dim:.................. 3
     codim:................ 1
     degree:............... 12
     multidegree:.......... T_0+T_1+T_2
     generators:........... (1,1,1)^1 
     purity:............... true
     dim sing. l.:......... -1
     Segre embedding:...... map to PP^10 ⊂ PP^11
i8 : describe XxY

o8 = ambient:.............. PP^2 x PP^1 x PP^1 x PP^2 x PP^1
     dim:.................. 4
     codim:................ 3
     degree:............... 240
     multidegree:.......... 2*T_0^2*T_2+2*T_0^2*T_3+2*T_0^2*T_4+3*T_0*T_1*T_2+3*T_0*T_1*T_3+3*T_0*T_1*T_4
     generators:........... (1,1,0,0,0)^1 (3,0,0,0,0)^1 (0,0,1,1,1)^1 (2,1,0,0,0)^1 
     purity:............... true
     dim sing. l.:......... -1
     Segre embedding:...... map to PP^54 ⊂ PP^71

See also