K3 -- make a lattice-polarized K3 surface

Synopsis

• Usage:

  K3(g,d,n)

  K3(g,d,n,CoefficientRing=>K)

• Inputs:
  • g, an integer
  • d, an integer
  • n, an integer
• Optional inputs:
  • CoefficientRing => ..., default value ZZ/65521
  • Singular => ..., default value null
  • Verbose => ..., default value false
• Outputs:
  • a K3 surface defined over $K$ with rank 2 lattice defined by the intersection matrix $\begin{pmatrix} 2g-2 & d \\ d & n \end{pmatrix}$

Description

i1 : K3(6,1,-2)

o1 = K3 surface with rank 2 lattice defined by the intersection matrix: | 10 1  |
                                                                        | 1  -2 |
     -- (1,0): K3 surface of genus 6 and degree 10 containing rational curve of degree 1 (GM fourfold) 
     -- (2,0): K3 surface of genus 21 and degree 40 containing rational curve of degree 2 


o1 : Lattice-polarized K3 surface

See also

• K3(ZZ) -- make a general K3 surface
• K3(String) -- show available functions to construct K3 surfaces of given genus
• LatticePolarizedK3surface Sequence -- image of the embedding of a K3 surface