# coefficientRing(LatticePolarizedK3surface) -- coefficient ring of a K3 surface

## Synopsis

• Function: coefficientRing
• Usage:
coefficientRing S
• Inputs:
• S,
• Outputs:
• a ring, the coefficient ring of $S$

## Description

 i1 : K = ZZ/3331 o1 = K o1 : QuotientRing i2 : S = K3(5,2,-2,CoefficientRing=>K) o2 = 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) o2 : Lattice-polarized K3 surface i3 : coefficientRing S o3 = K o3 : QuotientRing