i1 : quadroQuadricCremonaTransformation(5,23)
o1 = -- rational map --
source: Proj(QQ[x, y, z, t, u, v])
target: Proj(QQ[x, y, z, t, u, v])
defining forms: {
x*y,
2
x ,
2 2
- y*z + t + u ,
-x*t,
-x*u,
-x*v
}
o1 : RationalMap (Cremona transformation of PP^5 of type (2,2))
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i2 : describe oo
o2 = rational map defined by forms of degree 2
source variety: PP^5
target variety: PP^5
dominance: true
birationality: true
projective degrees: {1, 2, 2, 2, 2, 1}
number of minimal representatives: 1
dimension base locus: 3
degree base locus: 2
coefficient ring: QQ
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In addition, the four pairs (n,i)=(5,1),(8,1),(14,1),(26,1) correspond to the four examples of special quadro-quadric Cremona transformations:
i3 : describe quadroQuadricCremonaTransformation(5,1)
o3 = rational map defined by forms of degree 2
source variety: PP^5
target variety: PP^5
dominance: true
birationality: true
projective degrees: {1, 2, 4, 4, 2, 1}
number of minimal representatives: 1
dimension base locus: 2
degree base locus: 4
coefficient ring: QQ
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i4 : describe quadroQuadricCremonaTransformation(8,1)
o4 = rational map defined by forms of degree 2
source variety: PP^8
target variety: PP^8
dominance: true
birationality: true
number of minimal representatives: 1
dimension base locus: 4
degree base locus: 6
coefficient ring: QQ
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i5 : describe quadroQuadricCremonaTransformation(14,1)
o5 = rational map defined by forms of degree 2
source variety: PP^14
target variety: PP^14
dominance: true
birationality: true
number of minimal representatives: 1
dimension base locus: 8
degree base locus: 14
coefficient ring: QQ
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i6 : describe quadroQuadricCremonaTransformation(26,1)
o6 = rational map defined by forms of degree 2
source variety: PP^26
target variety: PP^26
dominance: true
birationality: true
number of minimal representatives: 1
dimension base locus: 16
degree base locus: 78
coefficient ring: QQ
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The object quadroQuadricCremonaTransformation is a method function.