K3(EmbeddedK3surface) -- make a lattice-polarized K3 surface from an embedded K3 surface

Synopsis

• Function: K3

• Usage:

  K3 S

• Inputs:
  • S, an embedded K3 surface, a special K3 surface that contains a curve $C$
• 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:
  • a K3 surface, the K3 surface $S$ with rank 2 lattice spanned by $H,C$, where $H$ is the hyperplane section class

Description

i1 : S = K3(3,5,-2);

o1 : Lattice-polarized K3 surface

i2 : S(1,1)

o2 = K3 surface of genus 7 and degree 12 in PP^7

o2 : Embedded K3 surface

i3 : T = K3 S(1,1)

o3 = K3 surface with rank 2 lattice defined by the intersection matrix: | 12 3  |
                                                                        | 3  -2 |


o3 : Lattice-polarized K3 surface

i4 : T(1,0)

o4 = K3 surface of genus 7 and degree 12 in PP^7

o4 : Embedded K3 surface