Macaulay2 » Documentation
Packages » K3Surfaces :: LatticePolarizedK3surface Sequence
next | previous | forward | backward | up | index | toc

# LatticePolarizedK3surface Sequence -- image of the embedding of a K3 surface

- Operator: SPACE
- Usage:
    `S(a,b)`
- Inputs:
  - S, a K3 surface, a lattice-polarized K3 surface with rank 2 lattice spanned by $H,C$
  - a sequence, a sequence of two integers (a,b)
- Outputs:
  - an embedded K3 surface, the image of the embedding of $S$ by the complete linear system $|a H + b C|$

## Description

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

    o1 = K3 surface with rank 2 lattice defined by the intersection matrix: | 8 2  |
                                                                            | 2 -2 |
         -- (1,0): K3 surface of genus 5 and degree 8 containing rational curve of degree 2
         -- (2,0): K3 surface of genus 17 and degree 32 containing rational curve of degree 4
         -- (2,1): K3 surface of genus 20 and degree 38 containing rational curve of degree 2 (cubic fourfold)
         -- (3,0): K3 surface of genus 37 and degree 72 containing rational curve of degree 6
         -- (3,1): K3 surface of genus 42 and degree 82 containing rational curve of degree 4 (GM fourfold)

    o1 : Lattice-polarized K3 surface

    i2 : S(1,0)

    o2 = K3 surface of genus 5 and degree 8 in PP^5

    o2 : Embedded K3 surface

    i3 : S(2,1)

    o3 = K3 surface of genus 20 and degree 38 in PP^20

    o3 : Embedded K3 surface

## See also

- map(LatticePolarizedK3surface,ZZ,ZZ) -- embedding of a K3 surface

## Ways to use this method:

- `EmbeddedK3surface Sequence`
- LatticePolarizedK3surface Sequence -- image of the embedding of a K3 surface

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/K3Surfaces.m2:975:0.