schemeInProduct -- multi-graded Ideal of the image of a map to a product of projective spaces

Synopsis

• Usage:

  J = schemeInProduct(I,maps,PP)

  J = schemeInProduct(I,maps)

• Inputs:
  • I, an ideal, defining the source scheme
  • maps, a list, list of sequences of polynomials each of a single degree, in I
  • PP, a ring, multigraded ring of the product of projective spaces
  • VariableName, a string, name of variable to use in constructing a ring PP if none is given
• Optional inputs:
  • VariableName => ..., default value X
• Outputs:
  • J, an ideal, multi-graded ideal of the image

Description

i1 : S = ZZ/101[a,b]

o1 = S

o1 : PolynomialRing

i2 : I = ideal 0_S

o2 = ideal 0

o2 : Ideal of S

i3 : f0 = matrix"a,b"

o3 = | a b |

             1       2
o3 : Matrix S  <--- S

i4 : f1 = matrix"a,b"

o4 = | a b |

             1       2
o4 : Matrix S  <--- S

i5 : maps = {f0,f1}

o5 = {| a b |, | a b |}

o5 : List

i6 : schemeInProduct(I, maps,VariableName =>"Y")

o6 = ideal(Y   Y    - Y   Y   )
            0,1 1,0    0,0 1,1

               ZZ
o6 : Ideal of ---[Y   ..Y   , a..b]
              101  0,0   1,1

See also

• productOfProjectiveSpaces -- Constructs the multi-graded ring of a product of copies of P^1 (pp is a synonym)