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SpecialFanoFourfolds :: specialCubicFourfold(Ideal)

specialCubicFourfold(Ideal) -- random special cubic fourfold

Synopsis

Description

i1 : use Grass(0,5,ZZ/33331);
i2 : -- quintic del Pezzo surface
     S = ideal(p_2*p_4-p_1*p_5, p_0*p_4-p_1*p_5-p_3*p_5+p_4*p_5, p_2*p_3-p_0*p_5, p_1*p_3-p_1*p_5-p_3*p_5+p_4*p_5, p_0*p_1-p_1*p_2-p_0*p_5+p_1*p_5);

                ZZ
o2 : Ideal of -----[p ..p ]
              33331  0   5
i3 : X = specialCubicFourfold(S,NumNodes=>0);

o3 : SpecialCubicFourfold (Cubic fourfold containing a surface of degree 5 and sectional genus 1)
i4 : discriminant X

o4 = 14

Some random cubic fourfolds can also be obtained by passing strings. For instance, an object as above is also given as follows.

i5 : specialCubicFourfold("quintic del Pezzo surface");

o5 : SpecialCubicFourfold (Cubic fourfold containing a surface of degree 5 and sectional genus 1)