# degree(LatticePolarizedK3surface,ZZ,ZZ) -- degree of a K3 surface

## Synopsis

• Function: degree
• Usage:
degree(S,a,b)
• Inputs:
• Outputs:
• an integer, the degree of $S$ embedded 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(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 : degree(S,2,1) o2 = 38