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

Synopsis

Function: map
Usage:

map(S,a,b)
Inputs:
- S, a K3 surface
- a, an integer
- b, an integer
Optional inputs:
- Degree => ..., default value null,
- DegreeLift => ..., default value null,
- DegreeMap => ..., default value null,
Outputs:
- the birational morphism defined by the complete linear system $|a H + b C|$, where $H,C$ is the basis of the lattice associated to $S$

Description

i1 : S = K3(3,1,-2)

o1 = K3 surface with rank 2 lattice defined by the intersection matrix: | 4 1  |
                                                                        | 1 -2 |
     -- (1,0): K3 surface of genus 3 and degree 4 containing rational curve of degree 1 
     -- (2,0): K3 surface of genus 9 and degree 16 containing rational curve of degree 2 
     -- (3,0): K3 surface of genus 19 and degree 36 containing rational curve of degree 3 
     -- (3,1): K3 surface of genus 21 and degree 40 containing rational curve of degree 1 
     -- (4,0): K3 surface of genus 33 and degree 64 containing rational curve of degree 4 
     -- (4,1): K3 surface of genus 36 and degree 70 containing rational curve of degree 2 


o1 : Lattice-polarized K3 surface

i2 : f = map(S,2,1);

o2 : MultirationalMap (rational map from surface in PP^3 to PP^10)

i3 : isMorphism f

o3 = true

i4 : degree f

o4 = 1

i5 : assert(image f == S(2,1))

Ways to use this method: