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

- 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

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/K3Surfaces.m2:898:0.