⋂ -- intersection of multi-projective varieties

i1 : K = ZZ/33331;

i2 : p = point PP_K^({1,2},{1,1});

o2 : ProjectiveVariety, a point in PP^1 x PP^2

i3 : X = random({1,1},p);

o3 : ProjectiveVariety, surface in PP^1 x PP^2

i4 : Y = random({2,1},p);

o4 : ProjectiveVariety, surface in PP^1 x PP^2

i5 : Z = random({2,2},p);

o5 : ProjectiveVariety, surface in PP^1 x PP^2

i6 : ⋂ {X,Y,Z}

o6 = 0-dimensional subvariety of PP^1 x PP^2 cut out by 10 hypersurfaces of multi-degrees (0,3)^2 (0,4)^1 (1,1)^1 (1,2)^1 (1,3)^1 (2,1)^1 (2,2)^1 (5,1)^1 (8,0)^1 

o6 : ProjectiveVariety, 0-dimensional subvariety of PP^1 x PP^2