unirationalParametrization -- unirational parametrization

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 0.998238s (cpu); 0.578263s (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

Ways to use unirationalParametrization:

unirationalParametrization(HodgeSpecialFourfold)
unirationalParametrization(SpecialCubicFourfold)
unirationalParametrization(SpecialCubicFourfold,EmbeddedProjectiveVariety)
unirationalParametrization(SpecialGushelMukaiFourfold)

For the programmer

The object unirationalParametrization is a method function.

The source of this document is in SpecialFanoFourfolds.m2:3488:0.

unirationalParametrization -- unirational parametrization

Description

See also

Ways to use unirationalParametrization:

For the programmer