specialGushelMukaiFourfold(surface,curve)
specialGushelMukaiFourfold(surface,curve,scroll)
specialGushelMukaiFourfold(surface,curve,K)
specialGushelMukaiFourfold(surface,curve,scroll,K)
From the returned fourfold $X$, with the following commands we obtain the surface $S$, the curve $C$, and the scroll $B$ used in the construction:
(B,C) = X.cache#"Construction"; S = ambientVariety C;
Then the surface $\overline{\psi_{B}(S)}\subset\mathbb{G}(1,4)$ can be constructed with
psi = rationalMap B; (psi S)%(image psi);
In the following example we construct a GM fourfold containing the image via $\psi_B:\mathbb{P}^6\dashrightarrow\mathbb{G}(1,4)$ of a quintic del Pezzo surface $S\subset\mathbb{P}^5\subset\mathbb{P}^6$, obtained as the image of the plane via the linear system of quartic curves with three general simple base points and two general double points, which cuts $B\simeq\mathbb{P}^1\times\mathbb{P}^2\subset\mathbb{P}^5\subset\mathbb{P}^6$ along a rational normal quartic curve obtained as the image of a general conic passing through the two double points.






