## Synopsis

• Usage:
• Inputs:
• n, an integer, the dimension of the projective space
• i, an integer, the i-th case in the classification for P^n (for instance, if n=5 then 1<=i<=39)
• K, a ring, the ground field (optional, the default value is QQ)
• Outputs:

## Description

 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)) 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

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 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 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 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