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, a rational map, whose target is a subvariety $Y\subset\mathbb{P}^n$
Outputs:
- a rational map, 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

Ways to use this method: