# pentagonalK3 -- pentagonal K3 surface

## Synopsis

• Usage:
pentagonalK3 g
• Inputs:
• Optional inputs:
• CoefficientRing => ..., default value ZZ/65521
• Outputs:
• , a random pentagonal K3 surface of genus $g$

## Description

 i1 : S = pentagonalK3 11 o1 = K3 surface with rank 2 lattice defined by the intersection matrix: | 20 5 | | 5 0 | -- (1,0): K3 surface of genus 11 and degree 20 containing elliptic curve of degree 5 (GM fourfold) -- (1,1): K3 surface of genus 16 and degree 30 containing elliptic curve of degree 5 -- (1,2): K3 surface of genus 21 and degree 40 containing elliptic curve of degree 5 -- (1,3): K3 surface of genus 26 and degree 50 containing elliptic curve of degree 5 (GM fourfold) -- (1,4): K3 surface of genus 31 and degree 60 containing elliptic curve of degree 5 -- (1,5): K3 surface of genus 36 and degree 70 containing elliptic curve of degree 5 -- (1,6): K3 surface of genus 41 and degree 80 containing elliptic curve of degree 5 -- (2,0): K3 surface of genus 41 and degree 80 containing elliptic curve of degree 10 o1 : Lattice-polarized K3 surface i2 : S' = S(1,0); o2 : Embedded K3 surface i3 : map(S',0,1) o3 = multi-rational map consisting of one single rational map source variety: K3 surface of genus 11 and degree 20 in PP^11 target variety: PP^1 o3 : MultirationalMap (rational map from S' to PP^1)