mapOntoImage -- the induced map from a variety to the closure of its image under a rational map

Synopsis

• Usage:

  h = mapOntoImage(f)

  psi = mapOntoImage(phi)

• Inputs:
  • f, a ring map, the ring map corresponding to a rational map $\phi$ of projective varieties
  • phi, an instance of the type RationalMapping, a rational map $\phi$ of projective varieties
• Optional inputs:
  • QuickRank => a Boolean value, default value true, whether to compute rank via the package FastMinors
• Outputs:
  • h, a ring map, the map of rings corresponding to $X \to \overline{\phi(X)}$.
  • psi, an instance of the type RationalMapping, the rational map

Description

i1 : R = QQ[x,y];

i2 : S = QQ[a,b,c];

i3 : f = map(R, S, {x^2, x*y, y^2});

o3 : RingMap R <-- S

i4 : mapOntoImage(f)

                 S       2        2
o4 = map (R, --------, {x , x*y, y })
              2
             b  - a*c

                       S
o4 : RingMap R <-- --------
                    2
                   b  - a*c

i5 : phi = rationalMapping f

                               2        2
o5 = Proj R - - - > Proj S   {x , x*y, y }

o5 : RationalMapping

i6 : mapOntoImage(phi)

                        /    S   \     2        2
o6 = Proj R - - - > Proj|--------|   {x , x*y, y }
                        | 2      |
                        \b  - a*c/

o6 : RationalMapping