specialCubicFourfold(String,Ring) -- random special cubic fourfold of a given type

Synopsis

• Function: specialCubicFourfold

• Usage:

  specialCubicFourfold(n,K)

  specialCubicFourfold n

• Inputs:
  • n, a string, the name of some known type of cubic fourfolds
  • K, a ring, the coefficient ring
• 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 special cubic fourfold of the indicated type over K

Description

i1 : X = specialCubicFourfold("3-nodal septic scroll",ZZ/65521);

o1 : ProjectiveVariety, cubic fourfold containing a surface of degree 7 and sectional genus 0

i2 : describe X

o2 = Special cubic fourfold of discriminant 26
     containing a 3-nodal surface of degree 7 and sectional genus 0
     cut out by 13 hypersurfaces of degree 3

See also

• specialCubicFourfold(EmbeddedProjectiveVariety) -- random special cubic fourfold