# super(RationalMap) -- get the rational map whose target is a projective space

## Synopsis

• Function: super
• Usage:
super phi
rationalMap(phi,Dominant=>null)
rationalMap phi
• Inputs:
• phi, , whose target is a subvariety $Y\subset\mathbb{P}^n$
• Outputs:
• , the composition of phi with the inclusion of $Y$ into $\mathbb{P}^n$

## Description

So that, for instance, if phi is a dominant map, then the code rationalMap(super phi,Dominant=>true) yields a map isomorphic to phi.

 i1 : phi = specialQuadraticTransformation 7; o1 : RationalMap (quadratic birational map from PP^8 to 8-dimensional subvariety of PP^10) i2 : phi' = super phi; o2 : RationalMap (quadratic rational map from PP^8 to PP^10) i3 : describe phi o3 = rational map defined by forms of degree 2 source variety: PP^8 target variety: complete intersection of type (2,2) in PP^10 dominance: true birationality: true projective degrees: {1, 2, 4, 8, 16, 22, 20, 12, 4} number of minimal representatives: 1 dimension base locus: 3 degree base locus: 10 coefficient ring: QQ i4 : describe phi' o4 = rational map defined by forms of degree 2 source variety: PP^8 target variety: PP^10 image: complete intersection of type (2,2) in PP^10 dominance: false birationality: false degree of map: 1 projective degrees: {1, 2, 4, 8, 16, 22, 20, 12, 4} number of minimal representatives: 1 dimension base locus: 3 degree base locus: 10 coefficient ring: QQ i5 : describe rationalMap(phi',Dominant=>true) o5 = rational map defined by forms of degree 2 source variety: PP^8 target variety: complete intersection of type (2,2) in PP^10 dominance: true birationality: true projective degrees: {1, 2, 4, 8, 16, 22, 20, 12, 4} number of minimal representatives: 1 dimension base locus: 3 degree base locus: 10 coefficient ring: QQ