mapToProjectiveSpace -- compute the map to projective space associated with the global sections of a Cartier divisor

Synopsis

• Usage:

  mapToProjectiveSpace( D )

• Inputs:
  • D, an instance of the type WeilDivisor,
• Optional inputs:
  • KnownCartier => a Boolean value, default value true, specify whether the divisor is known to be Cartier
  • Variable => a symbol, default value "YY"
  • Variable => a string, default value "YY", specify the variable to use in the construction of the target projective space
• Outputs:
  • a ring map,

Description

i1 : R = QQ[x,y,u,v]/ideal(x*y-u*v);

i2 : D = divisor( ideal(x, u) )

o2 = Div(x, u)

o2 : WeilDivisor on R

i3 : mapToProjectiveSpace(D)

o3 = map (R, QQ[YY ..YY ], {v, x})
                  1    2

o3 : RingMap R <-- QQ[YY ..YY ]
                        1    2

i4 : R = ZZ/7[x,y,z];

i5 : D = divisor(x*y)

o5 = Div(y) + Div(x)

o5 : WeilDivisor on R

i6 : mapToProjectiveSpace(D, Variable=>"Z")

             ZZ            2             2        2
o6 = map (R, --[Z ..Z ], {x , x*y, x*z, y , y*z, z })
              7  1   6

                   ZZ
o6 : RingMap R <-- --[Z ..Z ]
                    7  1   6

See also

• isCartier -- whether a Weil divisor is Cartier