unirationalParametrization -- unirational parametrization

Synopsis

• Usage:

  unirationalParametrization X

• Inputs:
  • X, a special cubic fourfold, or a special Gushel-Mukai fourfold
• Outputs:
  • a multi-rational map, a rational map of degree 2 from $\mathbb{P}^4$ to $X$

Description

The degree of the forms defining the returned map is 10 in the case of cubic fourfolds, and 26 in the case of GM fourfolds.

i1 : K = ZZ/10000019; S = PP_K^(2,2); -- Veronese surface;

o2 : ProjectiveVariety, surface in PP^5

i3 : X = specialCubicFourfold S;

o3 : ProjectiveVariety, cubic fourfold containing a surface of degree 4 and sectional genus 0

i4 : time f = unirationalParametrization X;
 -- used 1.42681s (cpu); 0.830142s (thread); 0s (gc)

o4 : MultirationalMap (rational map from PP^4 to X)

i5 : degreeSequence f

o5 = {[10]}

o5 : List

i6 : degree(f,Strategy=>"random point")

o6 = 2

See also

• parametrize(HodgeSpecialFourfold) -- rational parametrization
• parametrize(MultiprojectiveVariety) -- try to get a parametrization of a multi-projective variety