discriminant(SpecialCubicFourfold) -- discriminant of a special cubic fourfold

Synopsis

• Function: discriminant

• Usage:

  discriminant X

• Inputs:
  • X, a special cubic fourfold
• Optional inputs:
  • Algorithm => ..., default value null,
• Outputs:
  • an integer, the discriminant of $X$

Description

This calculation passes through the determination of the topological Euler characteristic of the surface contained in the fourfold, which is obtained thanks to the functions EulerCharacteristic and Euler (the option Algorithm allows you to select the method).

i1 : X = specialCubicFourfold "quintic del Pezzo surface";

o1 : ProjectiveVariety, cubic fourfold containing a surface of degree 5 and sectional genus 1

i2 : time discriminant X
 -- used 0.214456s (cpu); 0.111654s (thread); 0s (gc)

o2 = 14

See also

• discriminant(SpecialGushelMukaiFourfold) -- discriminant of a special Gushel-Mukai fourfold