# K3 -- make a lattice-polarized K3 surface

## Synopsis

• Usage:
K3(d,g,n)
K3(d,g,n,CoefficientRing=>K)
• Inputs:
• Optional inputs:
• CoefficientRing => ..., default value ZZ/65521
• Verbose => ..., default value true
• 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