K3(SpecialCubicFourfold) -- K3 surface associated to a cubic or GM fourfold

• Function: K3

• Usage:

  K3 X

• Inputs:
  • X, a special cubic fourfold, or a special Gushel-Mukai fourfold
• Optional inputs:
  • CoefficientRing => ..., default value ZZ/65521, make a lattice-polarized K3 surface
  • Singular => ..., default value null, make a lattice-polarized K3 surface
  • Verbose => ..., default value false, make a lattice-polarized K3 surface
• Outputs:
  • an embedded K3 surface, a K3 surface associated to $X$

i1 : X = specialFourfold "tau-quadric";

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

i2 : K3 X

o2 = K3 surface of genus 6 and degree 10 in PP^6

o2 : Embedded K3 surface

i3 : associatedK3surface X

o3 = surface in PP^6 cut out by 6 hypersurfaces of degree 2

o3 : ProjectiveVariety, K3 surface associated to X