family of schemes with fixed graded Betti numbers that contains both $C$ and $D$.

\(1) The fact that $V$ is an arithmetically Cohen-Macaulay, integral scheme of codimension $3$ follows from classical results, that can be found e.g. in [@br88]. In particular a minimal free resolution of the ideal $I_V$ is known, and the cardinality of a minimal system of generators of $I_V$ is $m={ {{t+2} \choose {2}} }$. Then the Artinian reduction of the coordinate ring of $V$ is good determinantal, as showed in Example \[artin\]. The divisor class group of $V$ is isomorphic to ${\mathbb{Z}}_2$ (see [@go77]). From knowledge of the graded Betti numbers of $I_V$ (see e.g. [@br88]), it follows that if $V$ was standard determinantal, then its degree matrix would have size $t\times (t+2)$ and all of its entries would be equal to $1$. The divisor class group of such a standard determinantal scheme is isomorphic to ${\mathbb{Z}}$ (see [@br75]). Therefore $V$ is not standard determinantal. Notice that if $t=2$ then $V$ is the Veronese surface in ${\mathbb{P}}^5$, which is not standard determinantal, since it is not isomorphic to a rational normal scroll surface.

\(2) Consider a special ${ {{t} \choose {2}} }$-th hyperplane section of $V$, 