In the following example, we define a Gushel-Mukai fourfold containing a so-called $\tau$-quadric.
i1 : K = ZZ/33331; ringP8 = K[x_0..x_8]; |
i3 : idealS = ideal(x_6-x_7, x_5, x_3-x_4, x_1, x_0-x_4, x_2*x_7-x_4*x_8); o3 : Ideal of ringP8 |
i4 : idealX = ideal(x_4*x_6-x_3*x_7+x_1*x_8, x_4*x_5-x_2*x_7+x_0*x_8, x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8, x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7, x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8, x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8); o4 : Ideal of ringP8 |
i5 : time X = specialGushelMukaiFourfold(idealS,idealX); -- used 1.61953 seconds o5 : SpecialGushelMukaiFourfold (Gushel-Mukai fourfold containing a surface of degree 2 and sectional genus 0) |
i6 : time describe X -- used 2.51689 seconds o6 = 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) |
The object specialGushelMukaiFourfold is a method function with options.