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K3Surfaces :: trigonalK3

trigonalK3 -- trigonal K3 surface

Synopsis

Description

See also the paper A remark on the generalized franchetta conjecture for K3 surfaces, by Beauville.

i1 : S = trigonalK3 11

o1 = K3 surface with rank 2 lattice defined by the intersection matrix: | 20 3 |
                                                                        | 3  0 |
     -- (1,0): K3 surface of genus 11 and degree 20 containing elliptic curve of degree 3 (GM fourfold) 
     -- (1,1): K3 surface of genus 14 and degree 26 containing elliptic curve of degree 3 (cubic fourfold) (GM fourfold) 
     -- (1,2): K3 surface of genus 17 and degree 32 containing elliptic curve of degree 3 
     -- (1,3): K3 surface of genus 20 and degree 38 containing elliptic curve of degree 3 (cubic fourfold) 
     -- (1,4): K3 surface of genus 23 and degree 44 containing elliptic curve of degree 3 
     -- (1,5): K3 surface of genus 26 and degree 50 containing elliptic curve of degree 3 (GM fourfold) 
     -- (1,6): K3 surface of genus 29 and degree 56 containing elliptic curve of degree 3 
     -- (1,7): K3 surface of genus 32 and degree 62 containing elliptic curve of degree 3 (cubic fourfold) 
     -- (1,8): K3 surface of genus 35 and degree 68 containing elliptic curve of degree 3 (GM fourfold) 
     -- (1,9): K3 surface of genus 38 and degree 74 containing elliptic curve of degree 3 (cubic fourfold) (GM fourfold) 
     -- (1,10): K3 surface of genus 41 and degree 80 containing elliptic curve of degree 3 
     -- (2,0): K3 surface of genus 41 and degree 80 containing elliptic curve of degree 6 
     -- (1,11): K3 surface of genus 44 and degree 86 containing elliptic curve of degree 3 (cubic fourfold) 


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)

See also

Ways to use trigonalK3 :

For the programmer

The object trigonalK3 is a method function with options.