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

Synopsis

• Function: discriminant

• Usage:

  discriminant X

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

Description

This function applies a formula given in Section 7 of the paper Special prime Fano fourfolds of degree 10 and index 2, obtaining the data required through the functions cycleClass, EulerCharacteristic and Euler (the option Algorithm allows you to select the method).

i1 : X = specialGushelMukaiFourfold "tau-quadric";

o1 : ProjectiveVariety, GM fourfold containing a surface of degree 2 and sectional genus 0

i2 : time discriminant X
 -- used 2.21766s (cpu); 0.833532s (thread); 0s (gc)

o2 = 10

See also

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