specialCubicFourfold(EmbeddedProjectiveVariety) -- random special cubic fourfold

• Function: specialCubicFourfold

• Usage:

  specialCubicFourfold S

  specialCubicFourfold(S,NumNodes=>n)

• Inputs:
  • S, an embedded projective variety, an irreducible surface in $\mathbb{P}^5$
• Optional inputs:
  • InputCheck => ..., default value 1, make a special cubic fourfold
  • NumNodes => ..., default value null, make a special cubic fourfold
  • Verbose => ..., default value false, request verbose feedback
• Outputs:
  • a special cubic fourfold, a random cubic fourfold containing the given surface

i1 : -- quintic del Pezzo surface
     S = surface({3,4},ZZ/33331);

o1 : ProjectiveVariety, surface in PP^5

i2 : X = specialCubicFourfold S;

o2 : ProjectiveVariety, cubic fourfold containing a surface of degree 5 and sectional genus 1

i3 : discriminant X

o3 = 14