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K3Surfaces :: LatticePolarizedK3surface Sequence

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

Synopsis

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

See also