specialGushelMukaiFourfold(String,Ring) -- random special Gushel-Mukai fourfold of a given type

• Function: specialGushelMukaiFourfold

• Usage:

  specialGushelMukaiFourfold(n,K)

  specialGushelMukaiFourfold n

• Inputs:
  • n, a string, the name of some known type of Gushel-Mukai fourfolds
  • K, a ring, the coefficient ring
• Optional inputs:
  • InputCheck => ..., default value 1, make a special Gushel-Mukai fourfold
  • Verbose => ..., default value false, request verbose feedback
• Outputs:
  • a special Gushel-Mukai fourfold, a random special Gushel-Mukai fourfold of the indicated type over K

i1 : X = specialGushelMukaiFourfold("cubic scroll",ZZ/65521);

o1 : ProjectiveVariety, GM fourfold containing a surface of degree 3 and sectional genus 0

i2 : describe X

o2 = Special Gushel-Mukai fourfold of discriminant 12
     containing a surface in PP^8 of degree 3 and sectional genus 0
     cut out by 7 hypersurfaces of degrees (1,1,1,1,2,2,2)
     and with class in G(1,4) given by 2*s_(3,1)+s_(2,2)
     Type: ordinary
     (case 7 of Table 1 in arXiv:2002.07026)