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SpecialFanoFourfolds :: unirationalParametrization

unirationalParametrization -- unirational parametrization

Synopsis

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 = ideal(random(3,Grass(0,5,K)), random(1,Grass(0,5,K)), random(1,Grass(0,5,K)));

o2 : Ideal of K[p ..p ]
                 0   5
i3 : X = specialCubicFourfold S;
-- computing number of nodes using a probabilistic method... 
-- got 0 nodes

o3 : SpecialCubicFourfold (Cubic fourfold containing a surface of degree 3 and sectional genus 1)
i4 : time f = unirationalParametrization X;
     -- used 0.59106 seconds

o4 : RationalMap (rational map from PP^4 to PP^5)
i5 : describe f

o5 = rational map defined by forms of degree 10
     source variety: PP^4
     target variety: PP^5
     image: smooth cubic hypersurface in PP^5
     dominance: false
     birationality: false
     coefficient ring: K
i6 : image f == ideal X

o6 = true
i7 : degreeMap f

o7 = 2

See also

Ways to use unirationalParametrization :

For the programmer

The object unirationalParametrization is a method function.