MultirationalMap | MultirationalMap -- product of multi-rational maps

Synopsis

• Operator: |

• Usage:

  Phi | Psi

• Inputs:
  • Phi, a multi-rational map, $\Phi:X \dashrightarrow Y$
  • Psi, a multi-rational map, $\Psi:X \dashrightarrow Z$
• Outputs:
  • a multi-rational map, the rational map $X \dashrightarrow Y\times Z$ defined by $p\mapsto (\Phi(p),\Psi(p))$; in other words, it is the map defined by the join of factor Phi with factor Psi

Description

i1 : Phi = rationalMap({veronese(1,2,ZZ/33331)},Dominant=>true);

o1 : MultirationalMap (dominant rational map from PP^1 to curve in PP^2)

i2 : Psi = rationalMap {veronese(1,3,ZZ/33331)};

o2 : MultirationalMap (rational map from PP^1 to PP^3)

i3 : (X,Y,Z) = (source Phi,target Phi,target Psi);

i4 : Eta = Phi | Psi;

o4 : MultirationalMap (rational map from X to Y x Z)

i5 : Eta | Phi;

o5 : MultirationalMap (rational map from X to Y x Z x Y)

i6 : Phi | Psi | Eta;

o6 : MultirationalMap (rational map from X to Y x Z x Y x Z)

i7 : super oo;

o7 : MultirationalMap (rational map from X to PP^2 x PP^3 x PP^2 x PP^3)

i8 : rationalMap(oo,image oo);

o8 : MultirationalMap (dominant rational map from X to curve in PP^2 x PP^3 x PP^2 x PP^3)

See also

• MultirationalMap || MultirationalMap -- product of multi-rational maps
• List | List -- join lists, sequences or arrays
• factor(MultirationalMap) -- the list of rational maps defining a multi-rational map
• MultiprojectiveVariety * MultiprojectiveVariety -- intersection of two multi-projective varieties
• super(MultirationalMap) -- get the multi-rational map whose target is a product of projective spaces