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 14.4578 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) |