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SpecialFanoFourfolds :: associatedK3surface(SpecialGushelMukaiFourfold)

associatedK3surface(SpecialGushelMukaiFourfold) -- associated K3 surface to a rational Gushel-Mukai fourfold

Synopsis

Description

Thus, the code image last associatedK3surface X gives the (minimal) associated K3 surface to X. For more details and notation, see the paper Trisecant Flops, their associated K3 surfaces and the rationality of some Fano fourfolds.

i1 : X = specialGushelMukaiFourfold "tau-quadric";

o1 : ProjectiveVariety, GM fourfold containing a surface of degree 2 and sectional genus 0
i2 : describe X

o2 = Special Gushel-Mukai fourfold of discriminant 10(')
     containing a surface in PP^8 of degree 2 and sectional genus 0
     cut out by 6 hypersurfaces of degrees (1,1,1,1,1,2)
     and with class in G(1,4) given by s_(3,1)+s_(2,2)
     Type: ordinary
     (case 1 of Table 1 in arXiv:2002.07026)
i3 : time (mu,U,C,f) = associatedK3surface X;
     -- used 7.12271 seconds
i4 : ? mu

o4 = multi-rational map consisting of one single rational map
     source variety: 5-dimensional subvariety of PP^8 cut out by 5 hypersurfaces of degree 2
     target variety: PP^4
     dominance: true
i5 : ? U

o5 = surface in PP^4 cut out by 9 hypersurfaces of degree 4
i6 : first C -- two disjoint lines

o6 = curve in PP^4 cut out by 5 hypersurfaces of degrees 1^1 2^4 

o6 : ProjectiveVariety, curve in PP^4 (subvariety of codimension 1 in U)

See also