LatticePolarizedK3surface Sequence -- image of the embedding of a K3 surface

Synopsis

• Operator: SPACE
• Usage:
S(a,b)
• Inputs:
• S, , a lattice-polarized K3 surface with rank 2 lattice spanned by $H,C$
• , a sequence of two integers (a,b)
• Outputs:
• , the image of the embedding of $S$ by the complete linear system $|a H + b C|$

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 : S(1,0) o2 = K3 surface of genus 5 and degree 8 in PP^5 o2 : Embedded K3 surface i3 : S(2,1) o3 = K3 surface of genus 20 and degree 38 in PP^20 o3 : Embedded K3 surface