MultiprojectiveVariety * MultiprojectiveVariety -- intersection of two multi-projective varieties

Synopsis

• Operator: *

• Usage:

  X * Y

• Inputs:
  • X, a multi-projective variety
  • Y, a multi-projective variety
• Outputs:
  • a multi-projective variety, the intersection of X and Y, that is, the projective variety defined by the sum of the corresponding ideals

Description

i1 : O = 0_(PP_(ZZ/101)^{2,1});

o1 : ProjectiveVariety, empty subscheme of PP^2 x PP^1

i2 : X = random({2,1},O);

o2 : ProjectiveVariety, surface in PP^2 x PP^1

i3 : Y = random({1,1},O);

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

i4 : X * Y

o4 = curve in PP^2 x PP^1 cut out by 3 hypersurfaces of multi-degrees (1,1)^1 (2,1)^1 (3,0)^1 

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

See also

• MultiprojectiveVariety + MultiprojectiveVariety -- union of two multi-projective varieties
• Ideal + Ideal -- sum of ideals
• ⋂(List) -- intersection of multi-projective varieties